Question

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

Answer 1

Answer:

55 degrees is more unusual in July as it is away from mean temperature as compared to January.

Step-by-step explanation:

We are given the following information in the question:

January:

Mean, μ = 36 degrees

Standard Deviation, σ = 10 degrees

July:

Mean, μ = 74 degrees

Standard Deviation, σ = 8 degrees

We calculate z scores corresponding to x = 55.

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

January:

$z_{score} = \displaystyle\frac{55-36}{10} = 1.9$

July:

$z_{score} = \displaystyle\frac{55-74}{8} = -2.375$

Thus, 55 degrees is more unusual in July as it is away from mean temperature as compared to January.