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Chapter 6: Q. 1.3 (page 385)
Flip a coin. If it's headed, roll a -sided die. If it's tails, roll an -sided die. Repeat this process times. Let the number of 's you roll.
The variable is not a binomial setting.
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45. Too cool at the cabin? During the winter months, the temperatures at the Stameses' Colorado cabin can stay well below freezing or for weeks at a time. To prevent the pipes from freezing, Mrs. Stames sets the thermostat at . She also buys a digital thermometer that records the indoor temperature each night at midnight. Unfortunately, the thermometer is programmed to measure the temperature in degrees Celsius. Based on several years' worth of data, the temperature in the cabin at midnight on a randomly selected night follows a Normal distribution with mean and standard deviation.
(a) Let the temperature in the cabin at midnight on a randomly selected night in degrees Fahrenheit (recall that . Find the mean and standard deviation of .
(b) Find the probability that the midnight temperature in the cabin is below . Show your work.
Rotter Partners is planning a major investment. The amount of profit (in millions of dollars) is uncertain, but an estimate gives the following probability distribution:
Based on this estimate, and
Rotter Partners owes its lender a fee of plus of the profits . So the firm actually retains from the investment. Find the mean and standard deviation of the amount that the firm actually retains from the investment.
To introduce her class to binomial distributions, Mrs. Desai gives a -item, multiple choice quiz. The catch is, 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.
Find . Explain what this result means.
A large auto dealership keeps track of sales and leases agreements made during each hour of the day. Let = the number of cars sold and = the number of cars leased during the 铿乺st hour of business on a randomly selected Friday. Based on previous records, the probability distributions of and are as follows:
顿别铿乶别 .
The dealership鈥檚 manager receives a bonus for each car sold and a bonus for each car leased. Find the mean and standard deviation of the difference in the manager鈥檚 bonus for cars sold and leased. Show your work.
What鈥檚 the expected number of cars in a randomly selected American household?
(a) Between and
(b)
(c)
(d)
(e)
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