Question

1. the data below show the number of hours of sleep ten students got last night: 4,5,6,6,7,7,8,8,9,10 a. find the percentile for the student who slept 7 hours. b. what percentile corresponds to the student who slept 9 hours?

Explanation:

Part a

Step1: Count values less than 7

We first count how many data points are less than 7. The data points are 4, 5, 6, 6. So there are 4 values less than 7.

Step2: Count total data points

The total number of data points \( n = 10 \).

Step3: Apply percentile formula

The formula for percentile of a value \( x \) is \( \text{Percentile}=\frac{\text{Number of values less than }x}{n}\times100 \).
Substituting the values, we get \( \text{Percentile}=\frac{4}{10}\times100 = 40 \).

Step1: Count values less than 9

We count how many data points are less than 9. The data points are 4, 5, 6, 6, 7, 7, 8, 8. So there are 8 values less than 9.

Step2: Count total data points

The total number of data points \( n = 10 \).

Step3: Apply percentile formula

Using the formula \( \text{Percentile}=\frac{\text{Number of values less than }x}{n}\times100 \).
Substituting the values, we get \( \text{Percentile}=\frac{8}{10}\times100 = 80 \).

Answer:

The percentile for the student who slept 7 hours is 40.

Part b