The state of California has a mean annual rainfall of 252 in

The state of California has a mean annual rainfall of 25.2 inches, whereas the state of New York has a mean annual rainfall of 46.3 inches. Assume the standard deviation for California is 4.9 inches and for New York is 3.1 inches. Find the probability that, for a sample of 35 years of rainfall for California, the mean annual rainfall is at least 26 inches.

Solution

mean = 25.2

s.d = 46.3

probability that the mean annual rainfall is at least 26 inches = P(X >= 26)

                                                                                                = P( (X-mean)/s.d >= (26 - 25.2)/46.3 )

                                                                                                = P(Z >= 0.0173)

                                                                                                = 1 - P(Z < 0.0173)

                                                                                                = 1 - 0.5080

                                                                                                = 0.4920 (ANS)