Suppose that the miles-per-gallon (mpg) rating of passenger cars is a normally distributed 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? (3 points)

b) What is the probability that a randomly selected passenger car gets between 30 and 35 mpg? (3 points)

c) An automobile manufacturer wants to build a new passenger car with an mpg rating that improves upon 99% of existing cars. What is the minimum mpg that would achieve this goal? (3 points)

d) A normal distribution is a widely used continuous probability distribution. Name two widely used discrete probability distributions? (1 point)