Question

use the accompanying radiation levels \\( \left( \frac { w } { k g } \
ight) \\) for 50 different cell phones. find the percentile \\( p _ { 70 } \\).
\\( p _ { 70 } = \square \frac { w } { k g } \\) (type an integer or decimal rounded to two decimal places as needed.)

Explanation:

Step1: Calculate the position of \(P_{70}\)

The formula for the position of the \(P_k\) percentile is \(L=\frac{k}{100}\times n\), where \(k = 70\) and \(n=50\).

$$L=\frac{70}{100}\times50=35$$

Step2: Find the value at the position

Since \(L = 35\) is an integer, the \(P_{70}\) value is the average of the 35th and 36th ordered data values.
Counting the data values (the data is already ordered):
The 35th value is \(1.25\) and the 36th value is \(1.26\)

$$P_{70}=\frac{1.25 + 1.26}{2}$$

$$P_{70}=\frac{2.51}{2}=1.255\approx1.26$$

Answer:

\(1.26\)