A major automobile company claims that its new model has an average rating of 25 mpg (miles per gallon). Company officials concede that some cars vary based on a variety of factors, and that the mpg performances have a standard deviation of 4 mpg. You are employed by a consumer protection group that routinely test-drives cars. Taking five cars at random off the assembly line, your group finds them to have a poor mpg performance defined as 20 mpg or below.
a. Assuming the company’s claim to be true (μ = 25 and σ = 4), what is the probability that a single car selected randomly performs poorly (mpg of 20 or below)?
b. Assuming the company’s claim to be true (μ = 25 and σ = 4), what is the probability that five cars selected randomly all perform poorly (mpg of 20 or below)?
c. Given the poor performance that your group observed with the five test cars, what conclusion can you draw about the company’s mpg claim?