Question

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 $22$pairs 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 with$22$ pairs of shoes or the boy with $22$ pairs of shoes? Explain.

Short answer

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

Part (a) Step 1. Given 

Part (a) Step 2. Concept

The formula used $z=\frac{x-mean}{s\tan darddeviation}$

Part (a) Step 3. Calculation

Only $5(13,13,13,15,19)$of the $20$pupils 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 $22$pairs of shoes is in the $25\%$ile. To put it another way, $25\%$of female students have fewer than$22$pairs of shoes. As a result,$25\%$ of the girl students have less than 22 pairs of shoes.

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.

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.