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Chapter 6: Q. 103 (page 406)
The mean number of s in a line digits long is
(a)
(b)
(c)
(d)
(e)
The mean number of s in a line digits long is an option (b) .
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Most states and Canadian provinces have government-sponsored lotteries. Here is a simple lottery wager, from the Tri-State Pick game that New Hampshire shares with Maine and Vermont. You choose a number with digits from to ; the state chooses a three-digit winning number at random and pays you if your number is chosen. Because there are numbers with three digits, you have a probability of of winning. Taking to be the amount your ticket pays you, the probability distribution of is
(a) Show that the mean and standard deviation of are and .
(b) If you buy a Pick 3 ticket, your winnings are , because it costs to play. Find the mean and standard deviation of . Interpret each of these values in context.
To introduce her class to binomial distributions, Mrs. Desai gives a 10 -item, multiple-choice quiz. The catch is, that students must simply guess an answer (A through E) for each question. Mrs. Desai uses her computer's random number generator to produce the answer key so that each possible answer has an equal chance to be chosen. Patti is one of the students in this class. Let the number of Patti's correct guesses.
1. Show that is a binomial random variable.
18. Life insurance
(a) It would be quite risky for you to insure the life of a -year-old friend under the terms of Exercise . There is a high probability that your friend would live and you would gain in premiums. But if he were to die, you would lose almost . Explain carefully why selling insurance is not risky for an insurance company that insures many thousands of -year-old men.
(b) The risk of an investment is often measured by the standard deviation of the return on the investment. The more variable the return is, the riskier the
investment. We can measure the great risk of insuring a single person’s life in Exercise by computing the standard deviation of the income Y that the insurer will receive. Find σY using the distribution and mean found in Exercise 14.
52. Study habits The academic motivation and study habits of female students as a group are better than those of males. The Survey of Study Habits and Attitudes is a psychological test that measures these factors. The distribution of scores among the women at a college has meanand standard deviation , and the distribution of scores among male students has mean and standard deviation You select a single male student and a single female student at random and give them the test.
(a) Explain why it is reasonable to assume that the scores of the two students are independent.
(b) What are the expected value and standard deviation of the difference (female minus male) between their scores?
(c) From the information given, can you find the probability that the woman chosen scores higher than the man? If so, find this probability. If not,
explain why you cannot.
54. The Tri -State Pick Refer to Exercise . Suppose
(a) Find the mean and standard deviation of your total winnings. Show your work.
(b) Interpret each of the values from (a) in context .
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