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Chapter 6: Q.4.2 (page 401)
Suppose you roll a pair of fair, six-sided dice until you get doubles. Let the number of rolls it takes.
Find . Interpret this result in context.
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(a) Explain whyis a binomial random variable.
(b) Find and interpret the expected value of.
(c) Find and interpret the standard deviation of.
Refer to Exercise . The ferry company鈥檚 expenses are per trip. Define the random variable to be the amount of profit (money collected minus expenses) made by the ferry company on a randomly selected trip. That is, .
(a) How does the mean of relate to the mean of ? Justify your answer. What is the practical importance of ?
(b) How does the standard deviation of relate to the standard deviation of ? Justify your answer. What is the practical importance of ?
85. Aircraft engines Engineers define reliability as the probability that an item will perform its function under specific conditions for a specific period of time. A certain model of aircraft engine is designed so that each engine has probability of performing properly for an hour of flight. Company engineers test an SRS of engines of this model. Let the number that operate for an hour without failure.
(a) Explain why is a binomial random variable.
(b) Find the mean and standard deviation of. Interpret each value in context.
(c) Two engines failed the test. Are you convinced that this model of engine is less reliable than it鈥檚 supposed to be? Compute and use the result to justify your answer.
76. Rhubarb Suppose you purchase a bundle of bare-root rhubarb plants. The sales clerk tells you that on average you can expect of the plants to die before producing any rhubarb. Assume that the bundle is a random sample of plants. Let the number of plants that die before producing any rhubarb. Use the binomial probability formula to find
Interpret this result in context.
Explain whether the given random variable has a binomial distribution.
Lefties Exactly of the students in a school are left-handed. Select students at random from the school, one at a time, until you find one who is left-handed. Let the number of students chosen.
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