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

Explanation:

Formula of z score :

`z=(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=(57-36)/(8)=2.625`

The mean high temperature in July =
`\mu_1=72^(\circ) F`

Standard deviation :
`\sigma_1=9^(\circ)F`

`z=(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.