Question

in the dominican republic in august, the distribution of daily high temperature is approximately normal with mean 86 degrees fahrenheit (°f). approximately 95% of all daily high temperatures are between 83°f and 89°f. what is the standard deviation of the distribution? 1°f 1 degree fahrenheit 1.5°f 1.5 degrees fahrenheit 2°f 2 degrees fahrenheit 3°f 3 degrees fahrenheit 6°f

Answer 1

The standard deviation of the distribution = 1.5°F

Given that the distribution of daily high temperature is approximately normal.

Population mean, $\mu$ = 86°F

Also approximately 95% of all daily high temperatures are between 83°F and 89°F.

So here $X_1$ = 83°F and $X_2$ = 89°F

We have the z - statistic ,

             $z=\frac{x-\mu}{\sigma}$

where $\sigma$ is the Standard deviation.

For 95% probability, the z-value for normal distribution is 1.96.

As we consider the positive z-value, take X =  $X_2$ =  89°F

So,   $z=\frac{x-\mu}{\sigma}$

⇒  $\sigma = \frac{x-\mu}{z} = \frac{89-86}{1.96} =1.53$ ≈ 1.5°F

So the standard deviation of the distribution = 1.5°F

Learn more about standard deviation at brainly.com/question/475676

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