Question

A state park has a normally distributed daytime temperatures in the month of June. The mean temperature is 75 Fahrenheit and then standard deviation of 7. What is the probability the temperature is above 82F?

Answer 1

Answer:

0.16

Step-by-step explanation:

This probability is the area under the standard normal curve to the right of 82.  Note that 82 is ONE standard deviation above the mean:  75 + 7 = 82.

According to the Empirical Rule, 68% of data lies within one standard deviation of the mean.  In other words, 34% lies between the mean and one standard deviation above the mean.  The remaining area under the standard normal curve is thus (100% - 68%), or 32%.  Half of that is 16%.  

The probability that the temperature is above 82, or above 1 standard deviation above the mean, is 16%, which we can also express as 0.16.

Alternatively, use a calculator with built-in statistical functions.  In this case the desired result is found by executing the following command:

normcdf(82, 10000, 75, 7).  The desired result is 0.1587, or approximately 0.16.