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Questions and Answers of Mathematics Economics Business

A binomial experiment consists of 500 trials. The probability of success for each trial is .4. What is the probability of obtaining the number of successes indicated in Problem? Approximate these
The probability of gene mutation under a given level of radiation is 3 × 10–5. What is the probability of at least 1 gene mutation if 105 genes are exposed to this level of radiation?
A binomial experiment consists of 500 trials. The probability of success for each trial is .4. What is the probability of obtaining the number of successes indicated in Problem? Approximate these
If the probability of a person contracting influenza on exposure is .6, consider the binomial distribution for a family of 6 that has been exposed. For this distribution,(A) Write the probability
A binomial experiment consists of 500 trials. The probability of success for each trial is .4. What is the probability of obtaining the number of successes indicated in Problem? Approximate these
The probability that a given drug will produce a serious side effect in a person using the drug is .02. In the binomial distribution for 450 people using the drug, what are the mean and standard
A binomial experiment consists of 500 trials. The probability of success for each trial is .4. What is the probability of obtaining the number of successes indicated in Problem? Approximate these
A multiple-choice test is given with 5 choices (only one is correct) for each of 10 questions. What is the probability of passing the test with a grade of 70% or better just by guessing?
A binomial experiment consists of 500 trials. The probability of success for each trial is .4. What is the probability of obtaining the number of successes indicated in Problem? Approximate these
An opinion poll based on a small sample can be unrepresentative of the population. To see why, assume that 40% of the electorate favors a certain candidate. If a random sample of 7 is asked their
A binomial experiment consists of 500 trials. The probability of success for each trial is .4. What is the probability of obtaining the number of successes indicated in Problem? Approximate these
A multiple-choice test is given with 5 choices (only one is correct) for each of 5 questions. Answering each of the 5 questions by guessing constitutes a binomial experiment with an associated
A binomial experiment consists of 500 trials. The probability of success for each trial is .4. What is the probability of obtaining the number of successes indicated in Problem? Approximate these
Graph equation (1) with σ = 5 and(A) μ = 10 (B) μ = 15 (C) μ = 20Graph all three in the same viewing window with Xmin = –10, Xmax = 40, Ymin = 0, and Ymax = 0.1.To graph Problem use a
The probability that a marriage will end in divorce within 10 years is .35. What are the mean and standard deviation for the binomial distribution involving 1,000 marriages?
Graph equation (1) with σ = 5 and(A) μ = 8 (B) μ = 12 (C) μ = 16Graph both in the same viewing window with Xmin = 0, Xmax = 40, Ymin = 0, and Ymax = 0.2.To graph Problem use a graphing
If the probability is .55 that a marriage will end in divorce within 20 years, what is the probability that out of 6 couples just married, in the next 20 years(A) None will be divorced?(B) All will
Graph equation (1) with μ = 20 and(A) σ = 2 (B) σ = 4Graph both in the same viewing window with Xmin = 0, Xmax = 40, Ymin = 0, and Ymax = 0.2.To graph Problem use a graphing calculator and
Graph equation (1) with μ = 18 and(A) σ = 3 (B) σ = 6Graph both in the same viewing window with Xmin = 0, Xmax = 40, Ymin = 0, and Ymax = 0.2.To graph Problem use a graphing calculator and
(A) If 120 scores are chosen from a normal distribution with mean 75 and standard deviation 8, how many scores x would be expected to satisfy 67 ≤ x ≤ 83?(B) Use a graphing calculator to generate
(A) If 250 scores are chosen from a normal distribution with mean 100 and standard deviation 10, how many scores x would be expected to be greater than 110?(B) Use a graphing calculator to generate
Salespeople for a solar technology company have average annual sales of $200,000, with a standard deviation of $20,000. What percentage of the salespeople would be expected to make annual sales of
The average lifetime for a car battery is 170 weeks, with a standard deviation of 10 weeks. If the company guarantees the battery for 3 years, what percentage of the batteries sold would be expected
A manufacturing process produces a critical part of average length 100 millimeters, with a standard deviation of 2 millimeters. All parts deviating by more than 5 millimeters from the mean must be
An automated manufacturing process produces a component with an average width of 7.55 centimeters, with a standard deviation of 0.02 centimeter. All components deviating by more than 0.05 centimeter
A union representative claims 60% of the union membership will vote in favor of a particular settlement. A random sample of 100 members is polled, and out of these, 47 favor the settlement. What is
The average healing time of a certain type of incision is 240 hours, with standard deviation of 20 hours. What percentage of the people having this incision would heal in 8 days or less? Assume a
The average height of a hay crop is 38 inches, with a standard deviation of 1.5 inches. What percentage of the crop will be 40 inches or more? Assume a normal distribution.
In a family with 2 children, the probability that both children are girls is approximately .25. In a random sample of 1,000 families with 2 children, what is the approximate probability that 220 or
In Problem 73, what is the approximate probability of the number of families with 2 girls in the sample being at least 225 and not more than 275? Approximate a binomial distribution with a normal
Scholastic Aptitude Tests (SATs) are scaled so that the mean score is 500 and the standard deviation is 100. What percentage of students taking this test should score 700 or more? Assume a normal
Candidate Harkins claims that she will receive 52% of the vote for governor. Her opponent, Mankey, finds that 470 out of a random sample of 1,000 registered voters favor Harkins. If Harkins’s claim
An instructor grades on a curve by assuming that grades on a test are normally distributed. If the average grade is 70 and the standard deviation is 8, find the test scores for each grade interval if
A test devised to measure aggressive–passive personalities was standardized on a large group of people. The scores were normally distributed with a mean of 50 and a standard deviation of 10. If we
Refer to the partially completed table of the six basic solutions to the e-systemFind basic solution (E). (A) (B) (C) (D) (E) (F) 2x1 + 5x2 + S₁ = 32 x₁ + 2x₂ + $₂ =
Repeat Example 1 for(A) The outcome is a number divisible by 12.(B) The outcome is an even number greater than 15.Data from Example 1Relative to the number wheel experiment (Fig. 1) and the sample
A single card is drawn from a standard 52-card deck. Let D be the event that the card drawn is a diamond, and let F be the event that the card drawn is a face card. In Problem, find the indicated
A black diamondRefer to the description of a standard deck of 52 cards and Figure 4 on page 384. An experiment consists of drawing 1 card from a standard 52-card deck. In Problem what is the
Odd or a multiple of 4In a lottery game, a single ball is drawn at random from a container that contains 25 identical balls numbered from 1 through 25. In Problem, use equation (1) to compute the
Even or a multiple of 7In a lottery game, a single ball is drawn at random from a container that contains 25 identical balls numbered from 1 through 25. In Problem, use equation (1) to compute the
Prime or greater than 20In a lottery game, a single ball is drawn at random from a container that contains 25 identical balls numbered from 1 through 25. In Problem, use equation (1) to compute the
A sum that is less than or equal to 5In Problem use the equally likely sample space in Example 2 to compute the probability of the following events:Data from Example 2Suppose that two fair dice are
A sum that is greater than 9In Problem use the equally likely sample space in Example 2 to compute the probability of the following events:Data from Example 2Suppose that two fair dice are
The number on the first die is a 6 or the number on the second die is a 3.In Problem use the equally likely sample space in Example 2 to compute the probability of the following events:Data from
The number on the first die is even or the number on the second die is even.In Problem use the equally likely sample space in Example 2 to compute the probability of the following events:Data from
In Problem solve the equation SP = S to find the stationary matrix S and the limiting matrix P̅. P= A B А .4 .6 B.2.8
Repeat Example 4 for the standard form P found in Matched Problem 3.Data from Example 4(A) Find the limiting matrix P for the standard form P̅ found in Example 3.(B) Use P̅ to find the limit of the
In Problem solve the equation SP = S to find the stationary matrix S and the limiting matrix P̅. A 4 A4 14. P B B 6 5 3 8 C 0 07 2 2
Problem refer to the regular Markov chain with transition matrixFor S = [.6 1.5], calculate SP. Is S a stationary matrix? Explain. P = .5 52 5 ∞o in .8
Problem refer to the regular Markov chain with transition matrixFor S = [0 0], calculate SP. Is S a stationary matrix? Explain. P = .5 52 5 ∞o in .8
Explain why an absorbing Markov chain that has more than one state is not regular.
Problem refer to the regular Markov chain with transition matrixFor S = [2/7 5/7] , calculate SP. Is S a stationary matrix? Explain. P = .5 52 5 ∞o in .8
A Markov chain has transition matrixFor S = [.3 .9], calculate SP. Is S a stationary matrix? Explain. 6 P = >- [48] 2
Explain why a regular Markov chain that has more than one state is not absorbing.
Find the mean for the sample measurements 3.2, 4.5, 2.8, 5.0, and 3.6.
For many sets of measurements the median lies between the mode and the mean. But this is not always so.(A) In a class of seven students, the scores on an exam were 52, 89, 89, 92, 93, 96, 99. Show
In Problem find the mean of the data set.5, 8, 6, 7, 9
Referring to Table 4 and the probability distribution just described, determine the probability that(A) A randomly drawn score is between 499.5 and 549.5.(B) A randomly drawn score is between 449.5
Repeat Example 1 for the following intervals:(A) 649.5–699.5 (B) 299.5–499.5Data from Example 1Referring to Table 4 and the probability distribution just described, determine the probability
Find the standard deviation for the sample measurements 1, 3, 5, 4, 3.
Find p and q for a single roll of a fair die, where success is a number divisible by 3 turning up.
Find the standard deviation for the sample measurements 1.2, 1.4, 1.7, 1.3, 1.5.
(A) When is the sample standard deviation of a set of measurements equal to 0?(B) Can the population standard deviation of a set of measurements ever be greater than the range? Explain why or why not.
In Problem find the indicated sum. 3 (x - 2)² if x₁ = 1, x₂ = 1₁x3 = 6 - i=1
(A) Using Figure 3, estimate the median annual income of a male with some college and a female who holds a bachelor’s degree. Within which educational category is there the greatest difference
(A) Construct a frequency table and histogram for the following data set using a class interval width of 2, starting at 0.5.(B) Construct a frequency table and histogram for the following data set
Compute the mean for the grouped sample data listed in Table 2. Table 2 Class Interval 0.5-5.5 5.5-10.5 10.5-15.5 15.5-20.5 Frequency 6 20 18 4
Find the mean for the sample measurements 3, 5, 1, 8, 6, 5, 4, and 6.
In Problem find the mean of the data set.12, 15, 18, 21
If we roll a fair die five times and identify a success in a single roll with a 1 turning up, what is the probability of the sequence SFFSS occurring?
Find the standard deviation for each set of grouped sample data. 8 2 9 4 10 Mean = 2 11 10 12 4 8 9 10 Mean = + 11 10 ++ 12
The weights (in pounds) were recorded for 20 kindergarten children chosen at random:(A) Use a graphing calculator to draw a histogram of the data, choosing the five class intervals 32.5 –37.5, 37.5
Twenty vehicles were chosen at random upon arrival at a vehicle emissions inspection station, and the time elapsed (in minutes) from arrival to completion of the emissions test was recorded for each
In Example 2, find the probability of the outcome FSSSF.Data from Example 2If we roll a fair die five times and identify a success in a single roll with a 1 turning up, what is the probability of the
In Problem find the indicated sum. Σ(x-10) ² if x₁ = 8, x₂ =9, x3 = 10, x₁ = 11, X5 = 12
Find the standard deviation for the grouped sample data shown below. 2 2 2 2 8 2 2 9 10 11 Mean = 10 + 12
(A) Using Figure 6, estimate the revenue and costs in 2017. In which years is a profit realized? In which year is the greatest loss experienced?(B) Using Figure 7, estimate the U.S. consumption of
(A) Construct a frequency table and histogram for the data set of part (A) of Problem 1 using a class interval width of 1, starting at 0.5.(B) Construct a frequency table and histogram for the data
Find the mean for the sample data summarized in Table 4 on page 504. Table 4 Frequency Table Class
Add the salary $100,000 to those in Example 3 and compute the median and mean for these eight salaries.Data from Example 3Find the median salary in the preceding list of seven salaries.
In Problem find the mean of the data set.–1, –2, 0, 2, 4
If a fair die is rolled five times, what is the probability of rolling(A) Exactly two 3’s?(B) At least two 3’s?
Using the same die experiment as in Example 3, what is the probability of rolling(A) Exactly one 3? (B) At least one 3?Data from Example 3If a fair die is rolled five times, what is the probability
In Problem find the indicated sum. Σ(x + 3)² if x₁ = −4₁ x₂ = -3₁ x3 = -2, x4 = -3
The graphing calculator command shown in Figure A generated a set of 400 random integers from 2 to 24, stored as list L1. The statistical plot in Figure B is a histogram of L1, using a class interval
An experiment consists of rolling a pair of dodecahedral (12-sided) dice and recording their sum (the sides of each die are numbered from 1 to 12). The command shown in Figure A simulated 500 rolls
Compute the median for the grouped data in Table 3. Table 3 Class Interval 3.5-4.5 4.5-5.5 5.5-6.5 6.5-7.5 7.5-8.5 8.5-9.5 Frequency 3 1 NWAN 2 4 3 2
Find the median for the grouped data in the following table: Class Interval 3.5-5.5 5.5-7.5 7.5-9.5 9.5-11.5 11.5-13.5 13.5-15.5 Frequency 423543
In Problem find the mean of the data set.85, 75, 65, 75
Use the binomial formula to expand (q + p)3.
In Problem find the indicated sum. 3 if i=1 x₁ = -20, x₂ = -15, x3 = -10 X1 (x + 15)²
Use the binomial formula to expand (q + p)4.
Graph the data in the following table using a bar graph. Gross Domestic Product (GDP) Year GDP (trillion $) 1975 5.49 1985 7.71 1995 10.28 14.37 16.49 2005 2015
In Problem find the indicated sum. 6 Ex; ifx = i + 3 for i = 1, 2, . . . , 6 i=1
Compute the mode(s), median, and mean for each data set:(A) 2, 1, 2, 1, 1, 5, 1, 9, 4 (B) 2, 5, 1, 4, 9, 8, 7(C) 8, 2, 6, 8, 3, 3, 1, 5, 1, 8, 3
In Problem find the indicated sum. 3 (x₁ - 4)² fi if x₁ = 0, x₂ = 4, X3 = 8, f₁ = 1,f₂ = 1, f3 = 1 XI
Graph the data in the following table using a bar graph. Corporation Revenues, 2015 Corporation Walmart ExxonMobil Apple Berkshire Hathaway McKesson United Health Revenue (billion
In Problem find the indicated sum. - Σx ifxi i=1 = 100i for i = 1, 2, ..., 5
Repeat Example 5, where the binomial experiment consists of two rolls of a die instead of three rolls.Data from Example 5Suppose a fair die is rolled three times and success on a single roll is
In Problem find the indicated sum. 3 Σ(x₁ - 4)²f; if x₁ = 0, x₂ = 4, X3 = 8,f₁ = 2,f₂ = 1, f3 = 2 =

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