A town's January high temperatures average 36°F with a standard deviation of 10°, while in July the mean high temperature is 74° and the standard deviation is 8°. In which month is it more unusual to have a day with a high temperature of 55°?

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Answer 1 · 2018-03-22T17:29:28

July

Find and compare the z-scores of January and July. The z-score formula is:
#z=(x-mu)/sigma#

January:
#z=(55-36)/10##=##1.9#

July:
#z=(55-74)/8=-2.375#

Since the z-score for July is #2.375# standard deviations away from its mean, it is more unusual to have a high temperature of 55 degrees.