Question

the dot - plot shows the heights (in inches) of the 25 students in mrs. nataros statistics class.
(a) find the percentile for lynette, the student who is 65 inches tall. (enter an integer.)
(b) ashers height is at the 88th percentile of the distribution. interpret this value. how tall is asher?
ashers height is less than 12% of the 25 students in mrs. nataros statistics class. asher is 74 inches tall.
ashers height is greater than 88% of the 25 students in mrs. nataros statistics class. asher is 88 inches tall.
ashers height is greater than 88% of the 25 students in mrs. nataros statistics class. asher is 74 inches tall.
ashers height is greater than 12% of the 25 students in mrs. nataros statistics class. asher is 63 inches tall.

Explanation:

Step1: Count number of students shorter than 65 inches

Count the dots to the left of 65 on the dot - plot. There are 5 students with heights 60, 62, and 64 inches.

Step2: Calculate the percentile

The formula for the percentile \(P\) is \(P=\frac{\text{number of values less than the given value}}{\text{total number of values}}\times100\). Here, the total number of students \(n = 25\), and the number of students shorter than 65 inches is 5. So \(P=\frac{5}{25}\times100 = 20\).

For part (b):
The \(k\)th percentile of a data - set is a value such that \(k\) percent of the data values are less than or equal to that value. If Asher's height is at the 88th percentile, it means that Asher's height is greater than 88% of the 25 students in the class.
Counting from the left on the dot - plot, we find that Asher's height is 74 inches.

Answer:

(a) 20
(b) Asher's height is greater than 88% of the 25 students in Mrs. Nataro's statistics class. Asher is 74 inches tall.