The 70-year long-term record for weather shows that for New York State, the annual precipitation has a mean of 39.96 inches and a standard deviation of 4.56 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 50.4 inches?
(b) What is the probability that next year the total precipitation for New York State is between 42.8 and 47.9 inches?
(c) What is the probability that next year the total precipitation for New York State is between 29.3 and 37.2 inches?
(d) What is the probability that next year the total precipitation for New York State is more than 34.4 inches?
(e) What is the probability that next year the total precipitation for New York State is less than 44.5 inches?
(f) What is the probability that next year the total precipitation for New York State is less than 31.4 inches?
An April 15, 2002 report in Time Magazine stated that the average age for women to marry in the United States is now 25.6 years of age. If the standard deviation is assumed to be 4.3 years, find the probability that a random sample of 32 U.S. women would show a mean age at marriage of less than or equal to 23.6 years. (Give your answer correct to four decimal places.)