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A​ town's January high temperatures average 39°F with a standard deviation of 10°​, while in July...

A​ town's January high temperatures average 39°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.

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 above 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 above the mean and a high temperature of 56°​ in January is only __ standard deviations above the mean.

Math   Statistics-And-Probability   
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Answer #1

The z scores for 56 in the 2 months is first computed as:

As the temperature 56 is 2 standard deviations away from the mean july temperature while only 1.7 standard deviations away from the mean temperature of january, therefore it is more unusual for july.

It is more unusual to have a day with a high temperature of 56°​ in July. A high temperature of 56°​ in July is 2 standard deviations above the mean and a high temperature of 56°​ in January is only 1.7 standard deviations above the mean.

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