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Illusion [34]
3 years ago
3

In the Dominican Republic in August, the distribution of daily high temperature is approximately normal with mean 86 degrees Fah

renheit ( °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?
Advanced Placement (AP)
1 answer:
aniked [119]3 years ago
6 0

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

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