stats question fuel efficiency

Question

Suppose that fuel efficiency for a particular model car under specified conditions is normally distributed with a mean value of 29.0 mpg and a standard deviation of 1.25 mpg. Let y = the fuel efficiency for a randomly selected car of this type.

QUESTION:

If three cars of this model are randomly selected, what is the probability that all three have efficiencies exceeding 31 mpg? (Round your answer to four decimal places.)

Answer 1

Each model exceeding a value (as opposed to averaging a value like a sample) should be the probability of each one of them exceeding the value - cubed. The models selected are independent of each other if the population is large. Look up P(z > (31-29)/1.25) and cube it.