Question

Suppose that you work for the EPA and, given the current fuel issues, are interested in the gas mileage of their new car the “Flash.” The manufacturers claim that the realized gas mileage for any individual car follows a normal distribution with mean of 32 and variance of 9. You randomly sample 36 of these cars to test out their mileage and find that they averaged 30 miles per gallon among them.

a. What is the probability that a randomly drawn car has a gas mileage of 28 miles per gallon or less? Greater than 33 miles per gallon? Please show your graphs.

b. Write down the sampling distribution implied by the population.

c. What is the probability that average miles per gallon for these cars was greater than 33 miles per gallon? What is the probability that the average miles per gallon were less than 28?

d. Explain why the probabilities from part 1 are different from part 3. (Hint: graphs might be helpful)

Answer 1