The 70-year long-term record for weather shows that for New York State, the annual precipitation has a mean of 39.84 inches and a standard deviation of 4.27 inches. The annual precipitation amount has a normal distribution. (Give your answers correct to four decimal places.)
(a) What is the probability that next year the total precipitation for New York State is more than 49.6 inches?
(b) What is the probability that next year the total precipitation for New York State is between 41.5 and 49 inches?
(c) What is the probability that next year the total precipitation for New York State is between 30.7 and 38.2 inches?
(d) What is the probability that next year the total precipitation for New York State is more than 36 inches?
(e) What is the probability that next year the total precipitation for New York State is less than 45.4 inches?
(f) What is the probability that next year the total precipitation for New York State is less than 31.6 inches?