Chapter 6: Q.70 (page 403)
Explain whether the given random variable has a binomial distribution
Long or short? Put the names of all the students in your class in a hat. Mix them up, and draw four names without looking. Let the number whose last names have more than six letters.
The given distribution is not binomial
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Benford’s law and fraud A not-so-clever employee decided to fake his monthly expense report. He believed that the first digits of his expense amounts should be equally likely to be any of the numbers from to . In that case, the first digit of a randomly selected expense amount would have the probability distribution shown in the histogram.
(a). Explain why the mean of the random variable Y is located at the solid red line in the figure.
(b) The first digits of randomly selected expense amounts actually follow Benford’s law (Exercise 5). What’s the expected value of the first digit? Explain how this information could be used to detect a fake expense report.
(c) What’s ? According to Benford’s law, what proportion of first digits in the employee’s expense amounts should be greater than ? How could this information be used to detect a fake expense report?
Better readers?() Did students have higher reading scores after participating in the chess program? Give appropriate statistical evidence to support your answer.
Predicting posttest scores() What is the equation of the linear regression model relating posttest and pretest scores? Define any variables used.
Based on the analysis in Exercise , the ferry company decides to increase the cost of a trip to . We can calculate the company’s profit on a randomly selected trip from the number of cars . Find the mean and standard deviation of. Show your work.
Toss times Suppose you toss a fair coin times. Let the number of heads you get.
(a) Find the probability distribution of.
(b) Make a histogram of the probability distribution. Describe what you see.
(c) Find and interpret the result.
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