Question

In the Dominican Republic in August, the distribution of daily high temperature is approximately normal with mean 86 degrees Fahrenheit ( °F °F ). Approximately 95% of all daily high temperatures are between 83°F 83°F and 89°F 89°F . What is the standard deviation of the distribution?

Answer 1

The standard deviation is 1.5

Step-by-step explanation:

Use the z-score formula to find the standard deviation.

`z = (x - \mu)/( \sigma)`

Using the empirical rule 95% falls within 2 standard deviations of the mean.

Using the upper limit, we have x=89 and

`\mu = 86`

We substitute and solve for the standard deviation.

`2= (89- 86)/( \sigma)`

This means

`\sigma= (89- 86)/( 2) = (3)/(2)`

`\sigma = 1.5`