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Shoes How many pairs of shoes do students have? Do girls have more shoes than boys? Here are data from a random sample of 20 female and 20 male students at a large high school:

(a) Find and interpret the percentile in the female distribution for the girl with 22pairs of shoes.

(b) Find and interpret the percentile in the male distribution for the boy with 22 pairs of shoes.

(c) Who is more unusual: the girl with22 pairs of shoes or the boy with 22 pairs of shoes? Explain.

Short Answer

Expert verified

Part (a) Here, 25% of the girl students have less than 22 pairs of shoes.

Part (b) Here, 85% of the male students have less than 22 pairs of shoes.

Part (c) The boy is more unusual

Step by step solution

01

Part (a) Step 1. Given 

02

Part (a) Step 2. Concept

The formula used z=x−meanstandarddeviation

03

Part (a) Step 3. Calculation

Only 5(13,13,13,15,19)of the 20pupils in the female distribution have pairs of shoes that are less than 22. As a result, the percentile is calculated as follows: 5/20=0.25=25%As a result, the girl with 22pairs of shoes is in the 25%ile. To put it another way, 25%of female students have fewer than22pairs of shoes. As a result,25% of the girl students have less than 22 pairs of shoes.

04

Part (b) Step 1. Calculation

From the above-mentioned sorted list, 17 of the 20 male students had pairs of shoes that are below 2. As a result, the appropriate percentile is calculated as follows: 17/20=0.85=85%

As a result, the youngster in the 85th percentile has 22 pairs of shoes. To put it another way, 85% of male students have fewer than 22 pairs of shoes. As a result, 85% of the male students have less than 22 pairs of shoes.

05

Part (c) Step 1. Calculation

The male is more unique because only 15% of boys have more than 22 pairs of shoes, but the girl's value is more evenly distributed over the distribution. Only 25% of girls have fewer, whereas 75% have the same number or more. Therefore, the boy is more unusual.

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