Chapter 2.1, Problem 1E

(a)

To determine

To find: the percentile in the female distribution for the girl with 22 pairs of shoes.

Answer to Problem 1E

Here, $25\%$ of the girl students have less than 22 pairs of shoes.

Explanation of Solution

Given:

  

Calculation:

From the above sorted list, only 5(13,13,13,15,19) of the 20 students in the female distribution have pairs of shoes below 22. Therefore, the corresponding percentile is computed as follows

  $\frac{5}{20}=0.25=25\%$

Hence, the girl with 22 pairs of shoes is at the ${25}^{\text{th }}$ percentile. In other words, $25\%$ of the girl students have less than 22 pairs of shoes.

Conclusion:

Hence, $25\%$ of the girl students have less than 22 pairs of shoes.

(b)

To determine

To find: the percentile in the male distribution for the boy with 22 pairs of shoes.

Answer to Problem 1E

Here, $85\%$ of the male students have less than 22 pairs of shoes.

Explanation of Solution

Given:

  

Calculation:

From the above sorted list, 17 of the 20 students in the male distribution have pairs of shoes below 2 . Therefore, the corresponding percentile is computed as follows:

  $\frac{17}{20}=0.85=85\%$

Hence, the boy with 22 pairs of shoes is at the ${85}^{\text{th }}$ percentile. In other words, $85\%$ of the male students have less than 22 pairs of shoes.

Conclusion:

Hence, $85\%$ of the male students have less than 22 pairs of shoes.

(c)

To determine

To find: whether the girl or the boy is unusual

Answer to Problem 1E

The boy is more unusual

Explanation of Solution

Given:

  

Calculation:

The boy is more unusual because only $15\%$ of the boys have more than 22 pairs of shoes than he has, while the girl has a value that is more centered in the distribution. Only $25\%$ of girls have fewer and $75\%$ have as many or more.

Conclusion:

Therefore, the boy is more unusual