Question

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?

Answer 1

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.