Posted by **sasha** on Saturday, January 5, 2013 at 9:13pm.

A survey of drivers in the United States found that 15% never use a cell phone while driving. Suppose that drivers arrive at random at an auto inspection station.

a. If the inspector checks 10 drivers, what is the probability that at least one driver never uses a cell phone while driving?

b. Suppose the inspector checks 1000 drivers. Use the normal approximation to the binomial distribution to find the approximate probability that at least 13% of these drivers never use a cell phone while driving.

c. If the drivers are inspected sequentially as they arrive randomly at the inspection station, what is the probability that the first driver who uses a cell phone while driving is the third driver checked?

d. What is the expected number of drivers who must be checked to find the first who never uses a cell phone while driving?

e. What is the expected number of drivers who must be checked to find the first driver who uses a cell phone while driving?

f. If it costs $5 to question each driver, what is the expected cost and standard deviation of questioning up to and including the first driver who uses a cell phone while driving?

g. Will the cost of inspection in part f often exceed $15? Explain.

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