The amount of snowfall falling in a certain mountain range i

The amount of snowfall falling in a certain mountain range is normally distributed with a mean of 89 inches and a standard deviation of 16 inches. What is the probability that the mean annual snowfall during 64 randomly picked years will exceed 91.8 inches.

Please show me your work how you got the answer.

Solution

Z=(x-)/=(91.8-89)/16=0.175. P(X>=91.8)=P(Z>=0.175)=0.5-P(0<=Z<=0.175)=0.5-0.0675=0.4325.