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:

Step1: Recall the percentile formula

The formula for percentile \(P=\frac{i}{n}\times100\), where \(i\) is the number of values less than or equal to the given value and \(n\) is the total number of values. Here \(n = 10\).

Step2: Calculate the percentile for \(x = 7\)

For \(x = 7\), the number of values less than or equal to \(7\) is \(i=5\).

$$P=\frac{5}{10}\times100 = 50$$

Step3: Calculate the percentile for \(x = 9\)

For \(x = 9\), the number of values less than or equal to \(9\) is \(i = 8\).

$$P=\frac{8}{10}\times100=80$$

Answer:

a. The percentile for the student who slept \(7\) hours is \(50\).
b. The percentile for the student who slept \(9\) hours is \(80\).