The annual precipitation amounts in a certain mountain range are normally distributed with a mean of 91 inches, and a standard deviation of 14 inches. what is the probability that the mean annual precipitation during 49 randomly picked years will be less than 93.8 inches?

The sample std. dev. will be (14 inches) / sqrt(49), or (14 inches) / 7, or 2 inches.

Find the z score for 93.8 inches:
       93.8 inches - 91.0 inches          2.8 inches
z = = = 1.4
                    2 inches                         2 inches

Now find the area under the standard normal curve to the left of z = +1.4.

My calculator returns the following:

normalcdf(-100,1.4) = 0.919.  This is the probability that the mean annual precipitation during those 49 years will be less than 93.8 inches.