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Chapter 6: Q.105 (page 406)
In which of the following situations would it be appropriate to use a Normal distribution to approximate probabilities for a binomial distribution with the given values of n and p?
(a)
(b)
(c)
(d)
(e)
Because the required requirements are only met in option(c), option(c) is the correct response.
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Refer to the previous Check Your Understanding (page 390 ) about Mrs. Desai's special multiple-choice quiz on binomial distributions. We defined the number of Patti's correct guesses.
1. Find . Interpret this value in context.
Fire insurance Suppose a homeowner spends for a home insurance policy that will pay out if the home is destroyed by fire. Let the profit made by the company on a single policy. From previous data, the probability that a home in this area will be destroyed by fire is .
(a) Make a table that shows the probability distribution of Y.
(b) Compute the expected value of Y. Explain what this result means for the insurance company
Benford鈥檚 law and fraud Refer to Exercise 13. It might also be possible to detect an employee鈥檚 fake expense records by looking at the variability in the first digits of those expense amounts.
(a) Calculate the standard deviation 蟽Y. This gives us an idea of how much variation we鈥檇 expect in the employee鈥檚 expense records if he assumed that first digits from to were equally likely.
(b) Now calculate the standard deviation of first digits that follow Benford鈥檚 law (Exercise 5). Would using standard deviations be a good way to detect fraud? Explain.
Binomial setting? A binomial distribution will be approximately correct as a model for one of these two sports settings and not for the other. Explain why by briefly discussing both settings. (a) A National Football League kicker has made of his field-goal attempts in the past. This season he attempts field goals. The attempts differ widely in the distance, angle, wind, and so on. (b) A National Basketball Association player has made of his free-throw attempts in the past. This season he takes free throws. Basketball free throws are always attempted from feet away with no interference from other players
83. Random digit dialing Refer to Exercise 81. Let the number of calls that don鈥檛 reach a live person.
(a) Find the mean of . How is it related to the mean of ? Explain why this makes sense.
(b) Find the standard deviation of How is it related to the standard deviation of ? Explain why this makes sense
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