8 questions, some with parts 1. IQ Score Invest in market No. Investment Totals 1 893 4,682 5,575 2 1,327 8,959 10,286 3 2,110 9,519 11,629 4 5,387 19,584 24,971 5 8,108 24,602 32,710 6 10,121 20,108 30,229 7 6,602 11,361 17,963 8 5,161 7,079 12,240 9 4,488 4,899 9,387 Totals 44,197 110,793 154,990 A finance journal published a study of whether the decision to invest in the stock market is dependent on IQ. Information on a sample of 154,990 adults living in Finland formed the database for the study. An IQ score (from a low score of 1 to a high score of 9) was determined for each Finnish citizen as well as whether or not the citizen invested in the stock market. The following table gives the number of Finnish citizens in each IQ score/investment category. Suppose one of the 154,990citizens is selected at random. Complete parts a through f. a. What is the probability that the Finnish citizen invests in the stock market? The probability is (Round to the nearest thousandth as needed.) b. What is the probability that the Finnish citizen has an IQ score of 6 or higher? The probability is (Round to the nearest thousandth as needed.) c. What is the probability that the Finnish citizen invests in the stock market and has an IQ score of 6 or higher? The probability is (Round to the nearest thousandth as needed.) d. What is the probability that the Finnish citizen invests in the stock market or has an IQ score of 6 or higher? The probability is (Round to the nearest thousandth as needed.) e. What is the probability that the Finnish citizen does not invest in the stock market? The probability is (Round to the nearest thousandth as needed.) f. Are the events {Invest in the stock market} and {IQ score of 1} mutually exclusive? A. Yes, they are mutually exclusive because there are no Finnish citizens who invest in the stock market and have an IQ score of 1. B. Yes, they are mutually exclusive because there are Finnish citizens who invest in the stock market and have an IQ score of 1. C. No, they are not mutually exclusive because there are Finnish citizens who invest in the stock market and have an IQ score of 1. D. No, they are not mutually exclusive because the probability that a Finnish citizen invests in the stock market and has an IQ score of 1 is very small. 2. For two events, A and B, P(A)equals 0.2, P(B)equals 0.5, and P(A|B )equals 0.2 a. Find P (AB) = (Simplify your answer.) b. Find P(B|A) = (Simplify your answer.) 3. Physicians and pharmacists sometimes fail to inform patients adequately about the proper application of prescription drugs and about the precautions to take in order to avoid potential side effects. One method of increasing patients' awareness of the problem is for physicians to provide patient medication instruction (PMI) sheets. A local medical survey, however, has found that only 45% of the doctors who prescribe drugs frequently distribute PMI sheets to their patients. Assume that 45% of all patients receive the PMI sheet with their prescriptions and that 12% receive the PMI sheet and are hospitalized because of a drug-related problem. What is the probability that a person will be hospitalized for a drugrelated problem given that the person received the PMI sheet? The probability is (Round to three decimal places as needed.) 4. Consider the probability distribution for the random variable x shown here. Complete parts a through c below. X 30 40 P(x) 0.10 0.25 50 0.30 60 70 0.20 0.10 80 0.05 Calculate , 2, and = (Type an integer or a decimal.) 2= (Type an integer or a decimal.) = (Round to three decimal places as needed.) 5. If x is a binomial random variable, use the binomial probability table to find the probabilities below. a. b. c. d. e. f. P (x=2) for n = 10, p =0.2 P (x6) for n = 15, p = 0.4 P (x>1) for n = 5, p =0.7 P (x<4) for n = 15, p = 0.7 P(x8) for n = 25, p = 0.6 P (x=2) for n = 20, p = 0.3 p(x=2) = round 3 decimal places p (x6) = round 3 decimal places p (x>1) = round 3 decimal places p (x<4) = round 3 decimal places p(x8) = round 3 decimal places p (x=2) = round 3 decimal places 6. According to a consumer survey of young adults (18-24 years of age) who shop online, 15% own a mobile phone with internet access. In a random sample of 300 young adults who shop online, let x be the number who own a mobile phone with internet access. a. Explain why x is a binomial random variable (to a reasonable degree of approximation). Choose the correct explanation below. A. The experiment consists of n identical, dependent trials, where there are only two possible outcomes, S (for Success) and F (for Failure). B. The experiment consists of n identical, independent trials, where there are only two possible outcomes, S (for Success) and F (for Failure). The probability of S remains the same from trial to trial. The variable x is the number of S's in n trials. C. The experiment consists of n identical, dependent trials, with more than two possible outcomes. The probability that an event occurs varies from trial to trial. D. The experiment consists of n identical, independent trials, where there are only two possible outcomes, S (for Success) and F (for Failure). The probability of S varies from trial to trial. The variable x is the number of F's in n trials. b. What is the value of p? Interpret this value. P = (Type an integer or a decimal.) Choose the correct interpretation of p below. A. For any young adult, the probability that they own a mobile phone with internet access is np B. For any young adult, the probability that they own a mobile phone with internet access is p. C. For any young adult, the probability that they own a mobile phone with internet access is 1 minus p D. For any young adult, the probability that they do not own a mobile phone with internet access is p. c. What is the expected value of x? Interpret this value. E(x) = Choose the correct interpretation below. A. In a random sample of 300 young adults E(x) left parenthesis x right parenthesis is the largest possible number of young people surveyed that will own mobile phones with internet access. B. In a random sample of 300 young adults E(x) left parenthesis x right parenthesis will always be the number of young people surveyed that will own mobile phones with internet access. C. In a random sample of 300 young adults E(x) left parenthesis x right parenthesis is the average number of young people surveyed that will own mobile phones with internet access. D. In a random sample of 300 young adults E(x) left parenthesis x right parenthesis is the average number of young people surveyed that will not own mobile phones with internet access. 7. The chances of a tax return being audited are about 2 in 1,000 if an income is less than $100,000 and 28 in 1,000 if an income is $100,000 or more. Complete parts a through e. a. What is the probability that a taxpayer with income less than $100,000 will be audited? With income of $100,000 or more? P ( taxpayer with income less than $ 100 comma 000 is audited) (Type an integer or a decimal.) What is the probability that a taxpayer with income of $100,000 or more will be audited? P(taxpayer with income of $ 100,000 or higher is audited) (Type an integer or a decimal.) b. If five taxpayers with incomes under $100,000 are randomly selected, what is the probability that exactly one will be audited? That more than one will be audited? P(x=1) = (Round to four decimal places as needed.) What is the probability that more than one will be audited? P ( x >1) = (Round to four decimal places as needed.) c. Repeat part b assuming that five taxpayers with incomes of $100,000 or more are randomly selected. P(x =1)= (Round to four decimal places as needed.) What is the probability that more than one will be audited? P (x >1)= (Round to four decimal places as needed.) e. What assumptions did you have to make in order to answer these questions? A. We must assume that the variables are binomial random variables. We must assume that the trials are identical, the probability of success is the same from trial to trial, and that the trials are independent. B. We must assume that the variables are random variables. We must assume that the trials are identical, and the probability of success varies from trial to trial. C. We must assume that the variables are binomial random variables. We must assume that the trials are identical and dependent. D. We must assume that the variables are binomial random variables. We must assume that the trials are identical, the probability of success varies from trial to trial, and that the trials are dependent. 8. According to a certain golf association, the weight of the golf ball ball shall not be greater than 1.620 ounces (45.93 grams). The diameter of the ball shall not be less than 1.680 inches. The velocity of the ball shall not be greater than 250 feet per second. The golf association periodically checks the specifications of golf balls using random sampling. Three dozen of each kind are sampled, and if more than three do not meet size or velocity requirements, that kind of ball is removed from the golf association's approved list. Complete parts a and b. a. What assumptions must be made in order to use the binomial probability distribution to calculate the probability that a particular kind of golf ball will be removed? A. The experiment consists of n identical trials. The number of outcomes can vary. The probability of success can change. The trials are independent. B. The experiment consists of n identical trials. There are only two possible outcomes on each trial. The probability of success remains the same from trial to trial. The trials are independent. C. The experiment consists of n identical trials. There are only two possible outcomes on each trial. The probability of success can change from trial to trial. The trials are dependent What information must be known in order to use the binomial probability distribution to calculate the probability that a particular kind of golf ball will be removed? A. The percentage of that kind of golf ball that meets the velocity requirements B. The percentage of that kind of golf ball that meets all the requirements C. The percentage of that kind of golf ball that meets the size requirements D. The percentage of that kind of golf ball that fails to meet both size and velocity requirements b. Suppose 20% of all balls produced by a particular manufacturer are less than 1.680 inches in diameter, and assume that the number of such balls, x, in a sample of three dozen balls can be adequately characterized by a binomial probability distribution. Find the mean of the binomial distribution. (Round to the nearest tenth as needed.) = round to the nearest tenth Find the standard deviation of the binomial distribution. = round to the nearest thousandth 8 questions, some with parts 1. IQ Score Invest in market No. Investment Totals 1 893 4,682 5,575 2 1,327 8,959 10,286 3 2,110 9,519 11,629 4 5,387 19,584 24,971 5 8,108 24,602 32,710 6 10,121 20,108 30,229 7 6,602 11,361 17,963 8 5,161 7,079 12,240 9 4,488 4,899 9,387 Totals 44,197 110,793 154,990 A finance journal published a study of whether the decision to invest in the stock market is dependent on IQ. Information on a sample of 154,990 adults living in Finland formed the database for the study. An IQ score (from a low score of 1 to a high score of 9) was determined for each Finnish citizen as well as whether or not the citizen invested in the stock market. The following table gives the number of Finnish citizens in each IQ score/investment category. Suppose one of the 154,990citizens is selected at random. Complete parts a through f. a. What is the probability that the Finnish citizen invests in the stock market? The probability is 0.285 (Round to the nearest thousandth as needed.) 0.286 b. What is the probability that the Finnish citizen has an IQ score of 6 or higher? The probability is 0.450 (Round to the nearest thousandth as needed.)0.458 c. What is the probability that the Finnish citizen invests in the stock market and has an IQ score of 6 or higher? The probability is 0.170 (Round to the nearest thousandth as needed.)0.171 d. What is the probability that the Finnish citizen invests in the stock market or has an IQ score of 6 or higher? The probability is 0.565 (Round to the nearest thousandth as needed.)0.573 e. What is the probability that the Finnish citizen does not invest in the stock market? The probability is 0.715 (Round to the nearest thousandth as needed.) 0.714 f. Are the events {Invest in the stock market} and {IQ score of 1} mutually exclusive? C b A. Yes, they are mutually exclusive because there are no Finnish citizens who invest in the stock market and have an IQ score of 1. B. Yes, they are mutually exclusive because there are Finnish citizens who invest in the stock market and have an IQ score of 1. C. No, they are not mutually exclusive because there are Finnish citizens who invest in the stock market and have an IQ score of 1. D. No, they are not mutually exclusive because the probability that a Finnish citizen invests in the stock market and has an IQ score of 1 is very small. 2. For two events, A and B, P(A)equals 0.2, P(B)equals 0.5, and P(A|B )equals 0.2 a. Find P (AB) = 0.1(Simplify your answer.) b. Find P(B|A) = 0.5 (Simplify your answer.) 3. Physicians and pharmacists sometimes fail to inform patients adequately about the proper application of prescription drugs and about the precautions to take in order to avoid potential side effects. One method of increasing patients' awareness of the problem is for physicians to provide patient medication instruction (PMI) sheets. A local medical survey, however, has found that only 45% of the doctors who prescribe drugs frequently distribute PMI sheets to their patients. Assume that 45% of all patients receive the PMI sheet with their prescriptions and that 12% receive the PMI sheet and are hospitalized because of a drug-related problem. What is the probability that a person will be hospitalized for a drugrelated problem given that the person received the PMI sheet? The probability is 0.267 (Round to three decimal places as needed.) 0.333 4. Consider the probability distribution for the random variable x shown here. Complete parts a through c below. X 30 40 50 60 70 80 P(x) 0.10 0.25 0.30 0.20 0.10 0.05 Calculate , 2, and = 51 (Type an integer or a decimal.) 42 2= 169 (Type an integer or a decimal.) 166 = 13.000(Round to three decimal places as needed.) 5. If x is a binomial random variable, use the binomial probability table to find the probabilities below. a. b. c. d. e. f. P (x=2) for n = 10, p =0.2 P (x6) for n = 15, p = 0.4 P (x>1) for n = 5, p =0.7 P (x<4) for n = 15, p = 0.7 P(x8) for n = 25, p = 0.6 P (x=2) for n = 20, p = 0.3 0.302 0.609 0.969 0.000 0.999 0.028 p(x=2) = round 3 decimal places0.267 p (x6) = round 3 decimal places0.500 p (x>1) = round 3 decimal places0.263 p (x<4) = round 3 decimal places0.000 p(x8) = round 3 decimal places0.998 p (x=2) = round 3 decimal places0.190 6. According to a consumer survey of young adults (18-24 years of age) who shop online, 15% own a mobile phone with internet access. In a random sample of 300 young adults who shop online, let x be the number who own a mobile phone with internet access. a. Explain why x is a binomial random variable (to a reasonable degree of approximation). Choose the correct explanation below. B d A. The experiment consists of n identical, dependent trials, where there are only two possible outcomes, S (for Success) and F (for Failure). B. The experiment consists of n identical, independent trials, where there are only two possible outcomes, S (for Success) and F (for Failure). The probability of S remains the same from trial to trial. The variable x is the number of S's in n trials. C. The experiment consists of n identical, dependent trials, with more than two possible outcomes. The probability that an event occurs varies from trial to trial. D. The experiment consists of n identical, independent trials, where there are only two possible outcomes, S (for Success) and F (for Failure). The probability of S varies from trial to trial. The variable x is the number of F's in n trials. b. What is the value of p? Interpret this value. P = 0.15 (Type an integer or a decimal.) 0.31 Choose the correct interpretation of p below. B c A. For any young adult, the probability that they own a mobile phone with internet access is np B. For any young adult, the probability that they own a mobile phone with internet access is p. C. For any young adult, the probability that they own a mobile phone with internet access is 1 minus p D. For any young adult, the probability that they do not own a mobile phone with internet access is p. c. What is the expected value of x? Interpret this value. E(x) = 45 93 Choose the correct interpretation below. C A. In a random sample of 300 young adults E(x) left parenthesis x right parenthesis is the largest possible number of young people surveyed that will own mobile phones with internet access. B. In a random sample of 300 young adults E(x) left parenthesis x right parenthesis will always be the number of young people surveyed that will own mobile phones with internet access. C. In a random sample of 300 young adults E(x) left parenthesis x right parenthesis is the average number of young people surveyed that will own mobile phones with internet access. D. In a random sample of 300 young adults E(x) left parenthesis x right parenthesis is the average number of young people surveyed that will not own mobile phones with internet access. 7. The chances of a tax return being audited are about 2 in 1,000 if an income is less than $100,000 and 28 in 1,000 if an income is $100,000 or more. Complete parts a through e. a. What is the probability that a taxpayer with income less than $100,000 will be audited? With income of $100,000 or more? P ( taxpayer with income less than $ 100 comma 000 is audited) (Type an integer or a decimal.) 0.002 0.014 What is the probability that a taxpayer with income of $100,000 or more will be audited? P(taxpayer with income of $ 100,000 or higher is audited) (Type an integer or a decimal.) 0.028 0.039 b. If five taxpayers with incomes under $100,000 are randomly selected, what is the probability that exactly one will be audited? That more than one will be audited? P(x=1) = 0.0099 (Round to four decimal places as needed.) 0.048 What is the probability that more than one will be audited? P ( x >1) = 0.0000 (Round to four decimal places as needed.) 0.0006 c. Repeat part b assuming that five taxpayers with incomes of $100,000 or more are randomly selected. P(x =1)= 0.1249 (Round to four decimal places as needed.)0.1081 What is the probability that more than one will be audited?0.0044 P (x >1)= 0.0074 (Round to four decimal places as needed.)0.8978 e. What assumptions did you have to make in order to answer these questions? A A. We must assume that the variables are binomial random variables. We must assume that the trials are identical, the probability of success is the same from trial to trial, and that the trials are independent. B. We must assume that the variables are random variables. We must assume that the trials are identical, and the probability of success varies from trial to trial. C. We must assume that the variables are binomial random variables. We must assume that the trials are identical and dependent. D. We must assume that the variables are binomial random variables. We must assume that the trials are identical, the probability of success varies from trial to trial, and that the trials are dependent. 8. According to a certain golf association, the weight of the golf ball ball shall not be greater than 1.620 ounces (45.93 grams). The diameter of the ball shall not be less than 1.680 inches. The velocity of the ball shall not be greater than 250 feet per second. The golf association periodically checks the specifications of golf balls using random sampling. Three dozen of each kind are sampled, and if more than three do not meet size or velocity requirements, that kind of ball is removed from the golf association's approved list. Complete parts a and b. a. What assumptions must be made in order to use the binomial probability distribution to calculate the probability that a particular kind of golf ball will be removed? Ba A. The experiment consists of n identical trials. The number of outcomes can vary. The probability of success can change. The trials are independent. B. The experiment consists of n identical trials. There are only two possible outcomes on each trial. The probability of success remains the same from trial to trial. The trials are independent. C. The experiment consists of n identical trials. There are only two possible outcomes on each trial. The probability of success can change from trial to trial. The trials are dependent What information must be known in order to use the binomial probability distribution to calculate the probability that a particular kind of golf ball will be removed? Db A. The percentage of that kind of golf ball that meets the velocity requirements B. The percentage of that kind of golf ball that meets all the requirements C. The percentage of that kind of golf ball that meets the size requirements D. The percentage of that kind of golf ball that fails to meet both size and velocity requirements b. Suppose 20% of all balls produced by a particular manufacturer are less than 1.680 inches in diameter, and assume that the number of such balls, x, in a sample of three dozen balls can be adequately characterized by a binomial probability distribution. Find the mean of the binomial distribution. (Round to the nearest tenth as needed.) = 7.2 round to the nearest tenth9.0 Find the standard deviation of the binomial distribution. =2.4 round to the nearest thousandth2.766 1.) The ages of a group of 50 women are approximately normally distributed with a mean of 52 years and a standard deviation of 6 years. One woman is randomly selected from the group, and her age is observed. a. Find the probability that her age will fall between 54 and 59 years. b. Find the probability that her age will fall between 47 and 52 years. c. Find the probability that her age will be less than 34 years. d. Find the probability that her age will exceed 41 years. 2.) Almost all companies utilize some type of year-end performance review for their employees. Human Resources (HR) at a university's Health Science Center provides guidelines for supervisors rating their subordinates. For example, raters are advised to examine their ratings for a tendency to be either too lenient or too harsh. According to HR, "if you have this tendency, consider using a normal distributionlong dash 10% of employees (rated) exemplary, 20% distinguished, 40% competent, 20% marginal, and 10% unacceptable." Suppose you are rating an employee's performance on a scale of 1 (lowest) to 100 (highest). Also, assume the ratings follow a normal distribution with a mean of 55 and a standard deviation of 17 Complete parts a and b. a. What is the lowest rating you should give to an "exemplary" employee if you follow the university's HR guidelines? I cannot go to b until I answer a. 3.) Personnel tests are designed to test a job applicant's cognitive and/or physical abilities. A particular dexterity test is administered nationwide by a private testing service. It is known that for all tests administered last year, the distribution of scores was approximately normal with mean 74 and standard deviation 7.9 a. A particular employer requires job candidates to score at least 78 on the dexterity test. Approximately what percentage of the test scores during the past year exceeded 78? b. The testing service reported to a particular employer that one of its jobcandidate's scores fell at the 95th percentile of the distribution (i.e., approximately 95% of the scores were lower than the candidate's, and only 5% were higher). What was thecandidate's score? 4.) The characteristics of an industrial filling process in which an expensive liquid is injected into a container was investigated. The quantity injected per container is approximately normally distributed with mean 10 units and standard deviation 0.02 units. Each unit of fill costs $20 per unit. If a container contains less than 10 units (that is, is underfilled), it must be reprocessed at a cost of $9 A properly filled container sells for $245 Complete parts a through c. a. Find the probability that a container is under filled. I cannot go to b and c until I answer a. 5.) Suppose a random sample of n= 100 measurements is selected from a population with mean and standard deviation . For each of the following values of and , give the values xx and xx a. b. c. d. = 13, = 4 = 169, = 100 = 26, = 80 = 13, = 200 xx = xx = xx = xx = xx = xx = xx = xx = (Type an integer or a decimal.) 6.) A random sample of n = 64 observations is drawn from a population with a mean equal to 21and a standard deviation equal to 16 a. Give the mean and standard deviation of the (repeated) sampling distribution xx b. Describe the shape of the sampling distribution of . Does your answer depend on the sample size? c. Calculate the standard normal z-score corresponding to a value xx = 17.5 d. Calculate the standard normal z-score corresponding to a value of xx= 24 a. xx = xx = b. c. d. 7.) A random sample of n = 36 observations is drawn from a population with a mean equal to 18 and a standard deviation equal to 12 a. Find the probability that xx is less than 12 b. Find the probability that xx is greater than 23 c. Find the probability that xx falls between 12 and 20 8.) A random sample of n= 100 observations is selected from a population with = 29 and equals 21 Approximate the probabilities shown below. a. b. c. d. P(xx 28) P(22.1 xx 26.8 P(xx 28.2) P(xx 27.0) 9.) The average salary for a certain profession is $62,500. Assume that the standard deviation of such salaries is $25, 500. Consider a random sample of 80 people in this profession and let xx represent the mean salary for the sample. a. What is xx? \f8 questions, some with parts 1. IQ Score Invest in market No. Investment Totals 1 893 4,682 5,575 2 1,327 8,959 10,286 3 2,110 9,519 11,629 4 5,387 19,584 24,971 5 8,108 24,602 32,710 6 10,121 20,108 30,229 7 6,602 11,361 17,963 8 5,161 7,079 12,240 9 4,488 4,899 9,387 Totals 44,197 110,793 154,990 A finance journal published a study of whether the decision to invest in the stock market is dependent on IQ. Information on a sample of 154,990 adults living in Finland formed the database for the study. An IQ score (from a low score of 1 to a high score of 9) was determined for each Finnish citizen as well as whether or not the citizen invested in the stock market. The following table gives the number of Finnish citizens in each IQ score/investment category. Suppose one of the 154,990citizens is selected at random. Complete parts a through f. a. What is the probability that the Finnish citizen invests in the stock market? The probability is 0.285 (Round to the nearest thousandth as needed.) 0.286 b. What is the probability that the Finnish citizen has an IQ score of 6 or higher? The probability is 0.450 (Round to the nearest thousandth as needed.)0.458 c. What is the probability that the Finnish citizen invests in the stock market and has an IQ score of 6 or higher? The probability is 0.170 (Round to the nearest thousandth as needed.)0.171 d. What is the probability that the Finnish citizen invests in the stock market or has an IQ score of 6 or higher? The probability is 0.565 (Round to the nearest thousandth as needed.)0.573 e. What is the probability that the Finnish citizen does not invest in the stock market? The probability is 0.715 (Round to the nearest thousandth as needed.) 0.714 f. Are the events {Invest in the stock market} and {IQ score of 1} mutually exclusive? C b A. Yes, they are mutually exclusive because there are no Finnish citizens who invest in the stock market and have an IQ score of 1. B. Yes, they are mutually exclusive because there are Finnish citizens who invest in the stock market and have an IQ score of 1. C. No, they are not mutually exclusive because there are Finnish citizens who invest in the stock market and have an IQ score of 1. D. No, they are not mutually exclusive because the probability that a Finnish citizen invests in the stock market and has an IQ score of 1 is very small. 2. For two events, A and B, P(A)equals 0.2, P(B)equals 0.5, and P(A|B )equals 0.2 a. Find P (AB) = 0.1(Simplify your answer.) b. Find P(B|A) = 0.5 (Simplify your answer.) 3. Physicians and pharmacists sometimes fail to inform patients adequately about the proper application of prescription drugs and about the precautions to take in order to avoid potential side effects. One method of increasing patients' awareness of the problem is for physicians to provide patient medication instruction (PMI) sheets. A local medical survey, however, has found that only 45% of the doctors who prescribe drugs frequently distribute PMI sheets to their patients. Assume that 45% of all patients receive the PMI sheet with their prescriptions and that 12% receive the PMI sheet and are hospitalized because of a drug-related problem. What is the probability that a person will be hospitalized for a drugrelated problem given that the person received the PMI sheet? The probability is 0.267 (Round to three decimal places as needed.) 0.333 4. Consider the probability distribution for the random variable x shown here. Complete parts a through c below. X 30 40 50 60 70 80 P(x) 0.10 0.25 0.30 0.20 0.10 0.05 Calculate , 2, and = 51 (Type an integer or a decimal.) 42 2= 169 (Type an integer or a decimal.) 166 = 13.000(Round to three decimal places as needed.) 5. If x is a binomial random variable, use the binomial probability table to find the probabilities below. a. b. c. d. e. f. P (x=2) for n = 10, p =0.2 P (x6) for n = 15, p = 0.4 P (x>1) for n = 5, p =0.7 P (x<4) for n = 15, p = 0.7 P(x8) for n = 25, p = 0.6 P (x=2) for n = 20, p = 0.3 0.302 0.609 0.969 0.000 0.999 0.028 p(x=2) = round 3 decimal places0.267 p (x6) = round 3 decimal places0.500 p (x>1) = round 3 decimal places0.263 p (x<4) = round 3 decimal places0.000 p(x8) = round 3 decimal places0.998 p (x=2) = round 3 decimal places0.190 6. According to a consumer survey of young adults (18-24 years of age) who shop online, 15% own a mobile phone with internet access. In a random sample of 300 young adults who shop online, let x be the number who own a mobile phone with internet access. a. Explain why x is a binomial random variable (to a reasonable degree of approximation). Choose the correct explanation below. B d A. The experiment consists of n identical, dependent trials, where there are only two possible outcomes, S (for Success) and F (for Failure). B. The experiment consists of n identical, independent trials, where there are only two possible outcomes, S (for Success) and F (for Failure). The probability of S remains the same from trial to trial. The variable x is the number of S's in n trials. C. The experiment consists of n identical, dependent trials, with more than two possible outcomes. The probability that an event occurs varies from trial to trial. D. The experiment consists of n identical, independent trials, where there are only two possible outcomes, S (for Success) and F (for Failure). The probability of S varies from trial to trial. The variable x is the number of F's in n trials. b. What is the value of p? Interpret this value. P = 0.15 (Type an integer or a decimal.) 0.31 Choose the correct interpretation of p below. B c A. For any young adult, the probability that they own a mobile phone with internet access is np B. For any young adult, the probability that they own a mobile phone with internet access is p. C. For any young adult, the probability that they own a mobile phone with internet access is 1 minus p D. For any young adult, the probability that they do not own a mobile phone with internet access is p. c. What is the expected value of x? Interpret this value. E(x) = 45 93 Choose the correct interpretation below. C A. In a random sample of 300 young adults E(x) left parenthesis x right parenthesis is the largest possible number of young people surveyed that will own mobile phones with internet access. B. In a random sample of 300 young adults E(x) left parenthesis x right parenthesis will always be the number of young people surveyed that will own mobile phones with internet access. C. In a random sample of 300 young adults E(x) left parenthesis x right parenthesis is the average number of young people surveyed that will own mobile phones with internet access. D. In a random sample of 300 young adults E(x) left parenthesis x right parenthesis is the average number of young people surveyed that will not own mobile phones with internet access. 7. The chances of a tax return being audited are about 2 in 1,000 if an income is less than $100,000 and 28 in 1,000 if an income is $100,000 or more. Complete parts a through e. a. What is the probability that a taxpayer with income less than $100,000 will be audited? With income of $100,000 or more? P ( taxpayer with income less than $ 100 comma 000 is audited) (Type an integer or a decimal.) 0.002 0.014 What is the probability that a taxpayer with income of $100,000 or more will be audited? P(taxpayer with income of $ 100,000 or higher is audited) (Type an integer or a decimal.) 0.028 0.039 b. If five taxpayers with incomes under $100,000 are randomly selected, what is the probability that exactly one will be audited? That more than one will be audited? P(x=1) = 0.0099 (Round to four decimal places as needed.) 0.048 What is the probability that more than one will be audited? P ( x >1) = 0.0000 (Round to four decimal places as needed.) 0.0006 c. Repeat part b assuming that five taxpayers with incomes of $100,000 or more are randomly selected. P(x =1)= 0.1249 (Round to four decimal places as needed.)0.1081 What is the probability that more than one will be audited?0.0044 P (x >1)= 0.0074 (Round to four decimal places as needed.)0.8978 e. What assumptions did you have to make in order to answer these questions? A A. We must assume that the variables are binomial random variables. We must assume that the trials are identical, the probability of success is the same from trial to trial, and that the trials are independent. B. We must assume that the variables are random variables. We must assume that the trials are identical, and the probability of success varies from trial to trial. C. We must assume that the variables are binomial random variables. We must assume that the trials are identical and dependent. D. We must assume that the variables are binomial random variables. We must assume that the trials are identical, the probability of success varies from trial to trial, and that the trials are dependent. 8. According to a certain golf association, the weight of the golf ball ball shall not be greater than 1.620 ounces (45.93 grams). The diameter of the ball shall not be less than 1.680 inches. The velocity of the ball shall not be greater than 250 feet per second. The golf association periodically checks the specifications of golf balls using random sampling. Three dozen of each kind are sampled, and if more than three do not meet size or velocity requirements, that kind of ball is removed from the golf association's approved list. Complete parts a and b. a. What assumptions must be made in order to use the binomial probability distribution to calculate the probability that a particular kind of golf ball will be removed? Ba A. The experiment consists of n identical trials. The number of outcomes can vary. The probability of success can change. The trials are independent. B. The experiment consists of n identical trials. There are only two possible outcomes on each trial. The probability of success remains the same from trial to trial. The trials are independent. C. The experiment consists of n identical trials. There are only two possible outcomes on each trial. The probability of success can change from trial to trial. The trials are dependent What information must be known in order to use the binomial probability distribution to calculate the probability that a particular kind of golf ball will be removed? Db A. The percentage of that kind of golf ball that meets the velocity requirements B. The percentage of that kind of golf ball that meets all the requirements C. The percentage of that kind of golf ball that meets the size requirements D. The percentage of that kind of golf ball that fails to meet both size and velocity requirements b. Suppose 20% of all balls produced by a particular manufacturer are less than 1.680 inches in diameter, and assume that the number of such balls, x, in a sample of three dozen balls can be adequately characterized by a binomial probability distribution. Find the mean of the binomial distribution. (Round to the nearest tenth as needed.) = 7.2 round to the nearest tenth9.0 Find the standard deviation of the binomial distribution. =2.4 round to the nearest thousandth2.766 1.) The ages of a group of 50 women are approximately normally distributed with a mean of 52 years and a standard deviation of 6 years. One woman is randomly selected from the group, and her age is observed. a. Find the probability that her age will fall between 54 and 59 years. b. Find the probability that her age will fall between 47 and 52 years. c. Find the probability that her age will be less than 34 years. d. Find the probability that her age will exceed 41 years. 2.) Almost all companies utilize some type of year-end performance review for their employees. Human Resources (HR) at a university's Health Science Center provides guidelines for supervisors rating their subordinates. For example, raters are advised to examine their ratings for a tendency to be either too lenient or too harsh. According to HR, "if you have this tendency, consider using a normal distributionlong dash 10% of employees (rated) exemplary, 20% distinguished, 40% competent, 20% marginal, and 10% unacceptable." Suppose you are rating an employee's performance on a scale of 1 (lowest) to 100 (highest). Also, assume the ratings follow a normal distribution with a mean of 55 and a standard deviation of 17 Complete parts a and b. a. What is the lowest rating you should give to an "exemplary" employee if you follow the university's HR guidelines? I cannot go to b until I answer a. 3.) Personnel tests are designed to test a job applicant's cognitive and/or physical abilities. A particular dexterity test is administered nationwide by a private testing service. It is known that for all tests administered last year, the distribution of scores was approximately normal with mean 74 and standard deviation 7.9 a. A particular employer requires job candidates to score at least 78 on the dexterity test. Approximately what percentage of the test scores during the past year exceeded 78? b. The testing service reported to a particular employer that one of its jobcandidate's scores fell at the 95th percentile of the distribution (i.e., approximately 95% of the scores were lower than the candidate's, and only 5% were higher). What was thecandidate's score? 4.) The characteristics of an industrial filling process in which an expensive liquid is injected into a container was investigated. The quantity injected per container is approximately normally distributed with mean 10 units and standard deviation 0.02 units. Each unit of fill costs $20 per unit. If a container contains less than 10 units (that is, is underfilled), it must be reprocessed at a cost of $9 A properly filled container sells for $245 Complete parts a through c. a. Find the probability that a container is under filled. I cannot go to b and c until I answer a. 5.) Suppose a random sample of n= 100 measurements is selected from a population with mean and standard deviation . For each of the following values of and , give the values xx and xx a. b. c. d. = 13, = 4 = 169, = 100 = 26, = 80 = 13, = 200 xx = xx = xx = xx = xx = xx = xx = xx = (Type an integer or a decimal.) 6.) A random sample of n = 64 observations is drawn from a population with a mean equal to 21and a standard deviation equal to 16 a. Give the mean and standard deviation of the (repeated) sampling distribution xx b. Describe the shape of the sampling distribution of . Does your answer depend on the sample size? c. Calculate the standard normal z-score corresponding to a value xx = 17.5 d. Calculate the standard normal z-score corresponding to a value of xx= 24 a. xx = xx = b. c. d. 7.) A random sample of n = 36 observations is drawn from a population with a mean equal to 18 and a standard deviation equal to 12 a. Find the probability that xx is less than 12 b. Find the probability that xx is greater than 23 c. Find the probability that xx falls between 12 and 20 8.) A random sample of n= 100 observations is selected from a population with = 29 and equals 21 Approximate the probabilities shown below. a. b. c. d. P(xx 28) P(22.1 xx 26.8 P(xx 28.2) P(xx 27.0) 9.) The average salary for a certain profession is $62,500. Assume that the standard deviation of such salaries is $25, 500. Consider a random sample of 80 people in this profession and let xx represent the mean salary for the sample. a. What is xx? \f