EXAMPLE 37April in Georgia

The state of Georgia reports that the mean temperature statewide for the month of April is . Assume that the standard deviation is and that temperature in Georgia in April is normally distributed. Draw the normal curve for temperatures between 45.5°F and 77.5°F, and the corresponding curve. Find the probability that the temperature is between 45.5°F and 77.5°F in April in Georgia.

Solution

Here, we have and , giving us

In Figure 47, the area between and is the same as between and . In other words,

This is a Case 3 problem from Table 8 (page 355). The table tells us that the area to the left of is 0.0228, and the area to the left of is 0.9772. The area between −2 and 2 is then equal to . The probability that the temperature is between 45.5°F and 77.5°F in April in Georgia is 0.9544.