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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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20. Size of American households In government data, a household consists of all occupants of a dwelling unit, while a family consists of two or more persons who live together and are related by blood or marriage. So all families form households, but some households are not families. Here are the distributions of household size and family size in the United States:
Let X = the number of people in a randomly selected U.S. household and Y = the number of people in a randomly chosen U.S. family.
(a) Make histograms suitable for comparing the probability distributions of X and Y. Describe any differences that you observe.
(b) Find the mean for each random variable. Explain why this difference makes sense.
(c) Find the standard deviations of both X and Y. Explain why this difference makes sense.
Better readers?() Did students have higher reading scores after participating in the chess program? Give appropriate statistical evidence to support your answer.
Kids and toys Refer to Exercise 4. Calculate the mean of the random variable X and interpret this result in context.
50. Checking independence For each of the following situations, would you expect the random variables and to be independent? Explain your answers.
(a)is the rainfall (in inches) on November of this year, and is the rainfall at the same location on November of next year.
(b) is the amount of rainfall today, and is the rainfall at the same location tomorrow.
(c) is today's rainfall at the airport in Orlando, Florida, and is today's rainfall at Disney World just outside Orlando.
While he was a prisoner of war during World War II, John Kerrich tossed a coin times. He gotheads. If the coin is perfectly balanced, the probability of a head is .
(a) Find the mean and the standard deviation of the number of heads in tosses, assuming the coin is perfectly balanced.
(b) Explain why the Normal approximation is appropriate for calculating probabilities involving the number of heads in tosses.
(c) Is there reason to think that Kerrich鈥檚 coin was not balanced? To answer this question, use a Normal distribution to estimate the probability that tossing a balanced coin times would give a count of heads at least this far from (that is, at least heads or no more than heads
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