Suppose that the miles-per-gallon (mpg) rating of passenger cars is a normally distributed random variable with a mean and a standard deviation of 33.8 mpg and 3.5 mpg, respectively.

a. What is the probability that a randomly selected passenger car gets at least 40 mpg?

b. What is the probability that a randomly selected passenger car gets between 30 and 35 mpg?

c. An automobile manufacturer wants to build a new passenger car with an mpg rating that improves upon 99 percent of existing cars. What is the minimum mpg that would achieve this goal?