Question

a towns january high temperatures average 37°f with a standard deviation of 10°, while in july the mean high temperature is 74° and the standard deviation is 9°. in which month is it more unusual to have a day with a high temperature of 56°? explain. select the correct choice below and fill in the answer boxes within your choice. (round to three decimal places as needed.) a. it is more unusual to have a day with a high temperature of 56° in january. a high temperature of 56° in january is standard deviations above the mean and a high temperature of 56° in july is only standard deviations below the mean. b. it is more unusual to have a day with a high temperature of 56° in july. a high temperature of 56° in july is standard deviations below the mean and a high temperature of 56° in january is only standard deviations above the mean.

Explanation:

Step1: Calculate z - score for January

The z - score formula is $z=\frac{x-\mu}{\sigma}$, where $x$ is the value, $\mu$ is the mean, and $\sigma$ is the standard deviation. For January, $\mu = 37$, $\sigma=10$, and $x = 56$. So, $z_{January}=\frac{56 - 37}{10}=\frac{19}{10}=1.900$.

Step2: Calculate z - score for July

For July, $\mu = 74$, $\sigma = 9$, and $x = 56$. So, $z_{July}=\frac{56 - 74}{9}=\frac{- 18}{9}=-2.000$.
The larger the absolute - value of the z - score, the more unusual the value is. Since $| - 2.000|>|1.900|$, it is more unusual to have a high temperature of $56^{\circ}$ in July.

Answer:

B. It is more unusual to have a day with a high temperature of $56^{\circ}$ in July. A high temperature of $56^{\circ}$ in July is $2.000$ standard deviations below the mean and a high temperature of $56^{\circ}$ in January is only $1.900$ standard deviations above the mean.