Question

A​ town's January high temperatures average 36degreesF with a standard deviation of 8degrees​, while in July the mean high temperature is 72degrees and the standard deviation is 9degrees. In which month is it more unusual to have a day with a high temperature of 57degrees​? Explain.

Answer 1

Answer: July

Step-by-step explanation:

Formula of z score :

$z=\dfrac{X-\mu}{\sigma}$

Given: The mean high temperature in January = $\mu_1=36^{\circ} F$

Standard deviation : $\sigma_1=8^{\circ}F$

For X = $57^{\circ}F$

$z=\dfrac{57-36}{8}=2.625$

The mean high temperature in July = $\mu_1=72^{\circ} F$

Standard deviation : $\sigma_1=9^{\circ}F$

$z=\dfrac{57-72}{8}=-1.875$

⇒ 57° F is about 2.6 standard deviations above the mean of January high temperatures, and  57° F is about 1.9 standard deviations below the mean of July’s high temperatures.

A general rule says that z-scores lower than -1.96 or higher than 1.96 are considered unusual .

Hence, the 57˚F is  more unusual in January.