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Questions and Answers of Mathematics Economics Business

In Problem a fair coin is tossed four times. What is the probability of obtainingAt least three tails?
In Problem use Appendix C to find the area under the standard normal curve and above the given interval on the horizontal axis.[0.2, 1.8]Data from Appendix C Area under the Standard Normal
In Problem discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample.(A) If the data set x1, x2, . . . , xn has mean x̅, then the data set
In Problem a fair coin is tossed four times. What is the probability of obtainingTails on each of the first three tosses?
In Problem use Appendix C to find the area under the standard normal curve and above the given interval on the horizontal axis.[–∞, 0.1]Data from Appendix C Area under the Standard Normal
In Problem use Appendix C to find the area under the standard normal curve and above the given interval on the horizontal axis.[–2.1, –0.9]Data from Appendix C Area under the Standard Normal
In Problem discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample.(A) If X represents a binomial random variable with mean m, then P(X ≥
In Problem a fair coin is tossed four times. What is the probability of obtainingNo heads?
In Problem use Appendix C to find the area under the standard normal curve and above the given interval on the horizontal axis.[0.6, ∞)Data from Appendix C Area under the Standard Normal
If the probability of success in a single trial of a binomial experiment with 1,000 trials is .6, what is the probability of obtaining at least 550 and no more than 650 successes in 1,000 trials?
In Problem a fair coin is tossed four times. What is the probability of obtainingFour heads?
Given a normal distribution with mean 50 and standard deviation 6, find the area under the normal curve:(A) Between 41 and 62(B) From 59 on
In Problem construct a histogram for the binomial distribution P(x) = nCxpxqn – x, and compute the mean and standard deviation ifn = 3, p = 1/4
For the sample quiz scores in Problem 6, find the mean and standard deviation using the data(A) Without grouping.(B) Grouped, with class interval of width 2, starting at 9.5.Data from Problem 6Given
A data set is formed by recording the sums of 100 rolls of a pair of dice. A second data set is formed by again rolling a pair of dice 100 times but recording the product, not the sum, of the two
In Problem construct a histogram for the binomial distribution P(x) = nCxpxqn – x, and compute the mean and standard deviation ifn = 3, p = 3/4
In Problem given a normal distribution with mean -15 and standard deviation 10, find the number of standard deviations each measurement is from the mean. Express the answer as a positive number.–22
In Problem construct a histogram for the binomial distribution P(x) = nCxpxqn – x, and compute the mean and standard deviation ifn = 4, p = 1/3
In Problem given a normal distribution with mean -15 and standard deviation 10, find the number of standard deviations each measurement is from the mean. Express the answer as a positive number.6.4
A fair die is rolled five times. What is the probability of rolling(A) Exactly three 6’s?(B) At least three 6’s?
In Problem construct a histogram for the binomial distribution P(x) = nCxpxqn – x, and compute the mean and standard deviation ifn = 5, p = 1/3
In Problem given a normal distribution with mean -15 and standard deviation 10, find the number of standard deviations each measurement is from the mean. Express the answer as a positive number.–1.8
Two dice are rolled three times. What is the probability of getting a sum of 7 at least once?
In Problem construct a histogram for the binomial distribution P(x) = nCxpxqn – x, and compute the mean and standard deviation ifn = 5, p = 0
In Problem given a normal distribution with mean -15 and standard deviation 10, find the number of standard deviations each measurement is from the mean. Express the answer as a positive
Ten students take an exam worth 100 points.(A) Construct a hypothetical set of exam scores for the ten students in which both the median and the mode are 30 points higher than the mean.(B) Could the
In Problem construct a histogram for the binomial distribution P(x) = nCxpxqn – x, and compute the mean and standard deviation ifn = 4, p = 1
In Problem given a normal distribution with mean -15 and standard deviation 10, find the number of standard deviations each measurement is from the mean. Express the answer as a positive number.10.9
In the last presidential election, 39% of a city’s registered voters actually cast ballots.(A) In a random sample of 20 registered voters from that city, what is the probability that exactly 8
In Problem round answers to four decimal places. A fair die is rolled four times. Find the probability of obtainingA 6, 6, 5, and 5 in that order.
In Problem given a normal distribution with mean -15 and standard deviation 10, find the number of standard deviations each measurement is from the mean. Express the answer as a positive
A random variable represents the number of wins in a 12- game season for a football team that has a probability of .9 of winning any of its games.(A) Find the mean and standard deviation of the
In Problem round answers to four decimal places. A fair die is rolled four times. Find the probability of obtainingTwo 6’s and two 5’s in any order.
In Problem given a normal distribution with mean 25 and standard deviation 5, find the area under the normal curve from the mean to the indicated measurement.27.2
The daily number of bad checks received by a large department store in a random sample of 10 days out of the past year was 15, 12, 17, 5, 5, 8, 13, 5, 16, and 4. Find the(A) Mean(B) Median(C) Mode(D)
Find the mean, median, and/or mode, whichever are applicable, for the following employee cafeteria service survey: Drink Ordered with Meal Coffee Tea Milk Soft drink Milk
In Problem round answers to four decimal places. A fair die is rolled four times. Find the probability of obtainingExactly two 6’s.
In Problem round answers to four decimal places. A fair die is rolled four times. Find the probability of obtainingExactly three 6’s.
The weekly record of reported accidents in a large auto assembly plant in a random sample of 35 weeks from the past 10 years is listed below:(A) Construct a frequency and relative frequency table
In Problem given a normal distribution with mean 25 and standard deviation 5, find the area under the normal curve from the mean to the indicated measurement.12.8
In Problem round answers to four decimal places. A fair die is rolled four times. Find the probability of obtainingNo 6’s.
In Problem given a normal distribution with mean 25 and standard deviation 5, find the area under the normal curve from the mean to the indicated measurement.18.7
The scores on a screening test for new technicians are normally distributed with mean 100 and standard deviation 10. Find the approximate percentage of applicants taking the test who score(A) Between
In Problem round answers to four decimal places. A fair die is rolled four times. Find the probability of obtainingAt least two 6’s.
If a baseball player has a batting average of .350, what is the probability that the player will get the following number of hits in the next four times at bat?(A) Exactly 2 hits (B) At least 2 hits
In Problem given a normal distribution with mean 25 and standard deviation 5, find the area under the normal curve from the mean to the indicated measurement.28.3
A newspaper publisher claims that 70% of the people in a community read their newspaper. Doubting the assertion, a competitor randomly surveys 200 people in the community. Based on the publisher’s
If a true–false test with 10 questions is given, what is the probability of scoring(A) Exactly 70% just by guessing?(B) 70% or better just by guessing?
In Problem given a normal distribution with mean 25 and standard deviation 5, find the area under the normal curve from the mean to the indicated measurement.23.9
A small town has three doctors on call for emergency service. The probability that any one doctor will be available when called is .90. What is the probability that at least one doctor will be
A multiple-choice test consists of 10 questions, each with choices A, B, C, D, E (exactly one choice is correct). Which is more likely if you simply guess at each question: all your answers are
In Problem consider the normal distribution with mean 60 and standard deviation 12. Find the area under the normal curve and above the given interval on the horizontal axis.[48, 60]
If 60% of the electorate supports the mayor, what is the probability that in a random sample of 10 voters, fewer than half support her?
In Problem consider the normal distribution with mean 60 and standard deviation 12. Find the area under the normal curve and above the given interval on the horizontal axis.[60, 84]
Construct a histogram for each of the binomial distributions in Problem. Compute the mean and standard deviation for each distribution.P(x) = 6Cx(.4)x(.6)6 - x
In Problem consider the normal distribution with mean 60 and standard deviation 12. Find the area under the normal curve and above the given interval on the horizontal axis.[57, 63]
In Problem consider the normal distribution with mean 60 and standard deviation 12. Find the area under the normal curve and above the given interval on the horizontal axis.[54, 66]
Construct a histogram for each of the binomial distributions in Problem. Compute the mean and standard deviation for each distribution.P(x) = 6Cx(.6)x(.4)6 – x
In Problem consider the normal distribution with mean 60 and standard deviation 12. Find the area under the normal curve and above the given interval on the horizontal axis.(–∞, 54]
Construct a histogram for each of the binomial distributions in Problem. Compute the mean and standard deviation for each distribution.P(x) = 8Cx(.3)x(.7)8 – x
In Problem consider the normal distribution with mean 60 and standard deviation 12. Find the area under the normal curve and above the given interval on the horizontal axis.[63, ∞)
Construct a histogram for each of the binomial distributions in Problem. Compute the mean and standard deviation for each distribution.P(x) = 8Cx(.7)x(.3)8 – x
In Problem consider the normal distribution with mean 60 and standard deviation 12. Find the area under the normal curve and above the given interval on the horizontal axis.[51, ∞)
In Problem use a graphing calculator to construct a probability distribution table.A random variable represents the number of successes in 20 Bernoulli trials, each with probability of success p =
In Problem consider the normal distribution with mean 60 and standard deviation 12. Find the area under the normal curve and above the given interval on the horizontal axis.(–∞, 78]
In Problem use a graphing calculator to construct a probability distribution table.A random variable represents the number of successes in 20 Bernoulli trials, each with probability of success p =
In Problem discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample.The mean of a normal distribution is a positive real number.
In Problem a coin is loaded so that the probability of a head occurring on a single toss is 3/4. In five tosses of the coin, what is the probability of gettingAll heads or all tails?
In Problem discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample.The standard deviation of a normal distribution is a positive real
In Problem a coin is loaded so that the probability of a head occurring on a single toss is 3/4. In five tosses of the coin, what is the probability of gettingExactly 2 heads or exactly 2 tails?
In Problem discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample.If two normal distributions have the same mean and standard deviation,
Toss a coin three times or toss three coins simultaneously, and record the number of heads. Repeat the binomial experiment 100 times and compare your relative frequency distribution with the
In Problem discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample.If two normal distributions have the same mean, then they have the same
Roll a die three times or roll three dice simultaneously, and record the number of 5’s that occur. Repeat the binomial experiment 100 times and compare your relative frequency distribution with the
In Problem discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample.The area under a normal distribution and above the horizontal axis is
Find conditions on p that guarantee the histogram for a binomial distribution is symmetrical about x = n/2. Justify your answer.
In Problem discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample.In a normal distribution, the probability is 0 that a score lies more
Consider two binomial distributions for 1,000 repeated Bernoulli trials—the first for trials with p = .15, and the second for trials with p = .85. How are the histograms for the two distributions
In Problem use the rule-of-thumb test to check whether a normal distribution (with the same mean and standard deviation as the binomial distribution) is a suitable approximation for the binomial
A random variable represents the number of heads in ten tosses of a coin.(A) Find the mean and standard deviation of the random variable.(B) Use a graphing calculator to simulate 200 repetitions of
In Problem use the rule-of-thumb test to check whether a normal distribution (with the same mean and standard deviation as the binomial distribution) is a suitable approximation for the binomial
A random variable represents the number of times a sum of 7 or 11 comes up in ten rolls of a pair of dice.(A) Find the mean and standard deviation of the random variable.(B) Use a graphing calculator
In Problem use the rule-of-thumb test to check whether a normal distribution (with the same mean and standard deviation as the binomial distribution) is a suitable approximation for the binomial
Each year a company selects a number of employees for a management training program at a university. On average, 70% of those sent complete the program. Out of 7 people sent, what is the probability
In Problem use the rule-of-thumb test to check whether a normal distribution (with the same mean and standard deviation as the binomial distribution) is a suitable approximation for the binomial
If the probability of a new employee in a fast-food chain still being with the company at the end of 1 year is .6, what is the probability that out of 8 newly hired people,(A) 5 will still be with
In Problem use the rule-of-thumb test to check whether a normal distribution (with the same mean and standard deviation as the binomial distribution) is a suitable approximation for the binomial
A manufacturing process produces, on average, 6 defective items out of 100. To control quality, each day a sample of 10 completed items is selected at random and inspected. If the sample produces
In Problem use the rule-of-thumb test to check whether a normal distribution (with the same mean and standard deviation as the binomial distribution) is a suitable approximation for the binomial
In Problem use the rule-of-thumb test to check whether a normal distribution (with the same mean and standard deviation as the binomial distribution) is a suitable approximation for the binomial
A manufacturing process produces, on average, 3% defective items. The company ships 10 items in each box and wants to guarantee no more than 1 defective item per box. If this guarantee applies to
A manufacturing process produces, on average, 5 defective items out of 100. To control quality, each day a random sample of 6 completed items is selected and inspected. If success on a single trial
In Problem use the rule-of-thumb test to check whether a normal distribution (with the same mean and standard deviation as the binomial distribution) is a suitable approximation for the binomial
Each year a company selects 5 employees for a management training program at a university. On average, 40% of those sent complete the course in the top 10% of their class. If we consider an employee
The probability of success in a Bernoulli trial is p = .1. Explain how to determine the number of repeated trials necessary to obtain a binomial distribution that passes the rule-of-thumb test for
A tuberculosis patient is given a chest x-ray. Four tuberculosis x-ray specialists examine each x-ray independently. If each specialist can detect tuberculosis 80% of the time when it is present,
A pharmaceutical laboratory claims that a drug causes serious side effects in 20 people out of 1,000, on average. To check this claim, a hospital administers the drug to 10 randomly chosen patients
For a binomial distribution with n = 100, explain how to determine the smallest and largest values of p that pass the rule-of-thumb test for using a normal distribution as a suitable approximation.
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 brown-eyed parents, both with the recessive gene for blue eyes, will have a child with brown eyes is .75. If such parents have 5 children, what is the probability that they will

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