Suppose that fuel efficiency (miles per gallon, mpg) for a particular car model under specified conditions is normally distributed with a mean of 40.0 mpg and a standard deviation of 3.0 mpg.

1. What is the probability that the fuel efficiency for a randomly selected car of this model is between 39.5 and 40.5 mpg? Round answer to 3 decimal places.
2. What is the probability that the fuel efficiency for a randomly selected car of this model is less than 36 mpg? Round answer to 3 decimal places.
3. What is the minimum fuel efficiency required to be in the top 4% of all cars of this model? Round answer to 1 decimal place.
4. Suppose that, as part of the quality control for the company, a random sample of n = 25 cars of this model is selected, and the mean of the sample, x , is computed to estimate the mean for all cars of this model. What is the probability that the sampling error will be no larger than 1 mpg? Report your answer as a decimal, rounded to 3 decimal places.
5. Suppose that, as part of the quality control for the company, a random sample of n = 25 cars of this model is selected, and the mean of the sample, x , is computed to estimate the mean for all cars of this model. What is the probability that mean of the sample is between 39.5 and 40.5 mpg?