During an annual heating season, the average hydro bill for customers in homes in Fredericton, New Brunswick was $457, with a standard deviation of $80. Assume that the gas bills follow a normal distribution, and let X be a random variable for the gas bill amount of a randomly selected Fredericton home.
(a) What proportion of homes had a gas bill (1) over $382, and (2) between $497 and $537?
(b) What bill amount was exceeded by (1) only 3% of homes, and (2) by 93% of homes?