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

Answer:

The standard deviation is 1.5

Explanation:

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

$z = \frac{x - \mu}{ \sigma}$

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.

$2= \frac{89- 86}{ \sigma}$

This means

$\sigma= \frac{89- 86}{ 2} = \frac{3}{2}$

$\sigma = 1.5$