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:
$z = \frac{x - μ}{σ}$ $z=(x-mu)/sigma$

January:
$z = \frac{55 - 36}{10}$ $z=(55-36)/10$ $=$ $=$ $1.9$ $1.9$

July:
$z = \frac{55 - 74}{8} = - 2.375$ $z=(55-74)/8=-2.375$

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