7.54 Thirty percent of all automobiles undergoing an emissions inspection at a certain inspection station fail the inspection.

a. Among 15 randomly selected cars, what is the probability that at most five fail the inspection?

b. Among 15 randomly selected cars, what is the probability that between five and 10 (inclusive)

fail to pass inspection?

c. Among 25 randomly selected cars, what is the mean value of the number that pass inspection, and what is the standard deviation of the number that pass inspection?

d. What is the probability that among 25 randomly selected cars, the number that pass is within 1 standard deviation of the mean value? (Hint: See Example 7.21.)