2. The mean high temperature in July for a town in the Central Valley is 106. If the standard deviation is 2 degrees, what is the probability that the temperature will not reach 100 on a given day?

First we change the temperature to a z-score using the formula

where

x = 100

m = 106

s = 2

= -6/2 = -3

 

We look up the area which corresponds to a z-score of -3 in Table 1 and get

.0013

This is the probability that the temperature will be less than 100 which is what we want.