Recall from previous cases that an automaker has recently introduced a new midsize model and that we have used the sample of 50 mileages to estimate that the population of mileages of all cars of this type is normally distributed with a mean mileage equal to 31.56 mpg and a standard deviation equal to .798 mpg. Suppose that a competing automaker produces a midsize model that is somewhat smaller and less powerful than the new midsize model. The competitor claims, however, that its midsize model gets better mileages. Specifically, the competitor claims that the mileages of all its midsize cars are normally distributed with a mean mileage equal to 33 mpg and a standard deviation equal to .7 mpg. We assume that the claim is true, and we calculate the probability that the mileage, x, of a randomly selected competing midsize car will be between 32 mpg and 35 mpg. That is, we wish to find P(32 x 35).

The competing automaker claims that the population of mileages of all its midsize cars is normally distributed with mean and standard deviation =.7. Suppose that an independent testing agency randomly selects one of these cars and finds that it gets a mileage of 31.2 mpg when tested as prescribed by the EPA. Because the sample mileage of 31.2 mpg is less than the claimed mean , we have some evidence that contradicts the competing automaker's claim. To evaluate the strength of this evidence, calculate the probability that the mileage, x, of a randomly selected midsize car would be less than or equal to 31.2

Show all work.