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Chapter 6: Q. 43 (page 379)
Based on the analysis in Exercise , the ferry company decides to increase the cost of a trip to . We can calculate the company鈥檚 profit on a randomly selected trip from the number of cars . Find the mean and standard deviation of. Show your work.
The mean and standard deviation are
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25. Did you vote? A sample survey contacted an SRS of registered voters in Oregon shortly after an election and asked respondents whether they had voted. Voter records show that of registered voters had actually voted. We will see later that in repeated random samples of size , the proportion in the sample who voted (call this proportion V) will vary according to the Normal distribution with mean and standard deviation .
(a) If the respondents answer truthfully, what is ? This is the probability that the sample proportion estimates the population
proportion within .
(b) In fact, of the respondents said they had voted . If respondents answer truthfully, what is ? This probability is so small that it is good evidence that some people who did not vote claimed that they did vote.
53. The Tri - State Pick Refer to Exercise . Suppose you buy a ticket on each of two different days.
(a) Find the mean and standard deviation of the total payoff. Show your work.
(b) Find the mean and standard deviation of your total winnings. Interpret each of these values 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
Ana is a dedicated Skee Ballplayer (see photo) who always rolls for the -point slot. The probability distribution of Ana's score on a single roll of the ball is shown below. You can check that and .
(a) A player receives one ticket from the game for every points scored. Make a graph of the probability distribution for the random variable number of tickets Ana gets on a randomly selected throw. Describe its shape.
(b) Find and interpret .
(c) Compute and interpret .
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鈥檚 life in Exercise by computing the standard deviation of the income Y that the insurer will receive. Find 蟽Y using the distribution and mean found in Exercise 14.
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