A town\'s January high temperatures average 38 degree F with a standard deviatio

Question

A town's January high temperatures average 38 degree F with a standard deviation of 9 degree, while in July the mean high temperature is 77 degree and the standard deviation is 10 degree. In which month is it more unusual to have a day with a high temperature of 55 degree? 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 55 degree in January. A high temperature of 55 degree in January is standard deviations above the mean and a high temperature of 55 degree in July is only standard deviations below the mean. B. It is more unusual to have a day with a high temperature of 55 degree in July. A high temperature of 55 degree in July is standard deviations below the mean and a high temperature of 55 degree in January is only standard deviations above the mean.

Explanation / Answer

here z score =(X-mean)/std deviation

therefore for temerature 55 F ; zscore for January =(55-38)/9=1.889

and for temerature 55 F ; zscore for July =(55-77)/10=-2.2

as z score reflect that 55 F is farthest from mean of July in terms of std deviaiton

hence Option B is correct

It is more unusual to have a day with a high temperature of 55 F. A high temerature of 55 F in July is 2.2 std deviation below the mean and a high temperature of 55 F in January is only 1.889 std deviation above the mean.

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