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.

Accepted Solution

Answer: JulyStep-by-step explanation:Formula of z score :[tex]z=\dfrac{X-\mu}{\sigma}[/tex]Given: The mean high temperature in January = [tex]\mu_1=36^{\circ} F[/tex]Standard deviation : [tex]\sigma_1=8^{\circ}F[/tex]For X = [tex]57^{\circ}F[/tex][tex]z=\dfrac{57-36}{8}=2.625[/tex]The mean high temperature in July = [tex]\mu_1=72^{\circ} F[/tex]Standard deviation : [tex]\sigma_1=9^{\circ}F[/tex][tex]z=\dfrac{57-72}{8}=-1.875[/tex]⇒ 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.