Chapter 6, Problem 11E

To determine

To explain which month is more unusual to have a day with high temperature of 55⁰C.

Answer to Problem 11E

The more unusual temperature occurs in July.

Explanation of Solution

Given:

January temperature:

Temperature = $x$ = 55

Mean = $\mu$ = 36

Standard deviation = $\sigma$ =10

July temperature:

Temperature = $x$ = 55

Mean = $\mu$ = 74

Standard deviation = $\sigma$ =8

Formula:

  $z=\frac{x-\mu }{\sigma }$

The z-score for January is,

  $z=\frac{55-36}{10}=1.90$

The z-score for July is,

  $z=\frac{55-74}{8}=-2.375$

As per rule, the more unusual temperature said to be that temperature whose z-score is more away from zero. Therefore, -2.375 is far away from 0 or the absolute value 2.375 is larger than 1.90. Hence more unusual temperature occurs in July.