Question

use the accompanying radiation levels (in $\frac{w}{kg}$) for 50 different cell phones. find the percentile corresponding to 1.10 $\frac{w}{kg}$. click the icon to view the radiation levels. the percentile corresponding to 1.10 $\frac{w}{kg}$ is (round to the nearest whole number as needed.)

Explanation:

Step1: Sort the data

The data is already sorted in ascending - order as given: 0.24, 0.29, 0.33, 0.44, 0.58, 0.61, 0.62, 0.64, 0.75, 0.80, 0.86, 0.92, 0.93, 0.94, 0.95, 0.97, 0.99, 1.02, 1.04, 1.08, 1.09, 1.10, 1.11, 1.12, 1.13, 1.14, 1.18, 1.18, 1.21, 1.21, 1.22, 1.24, 1.24, 1.25, 1.26, 1.27, 1.27, 1.28, 1.30, 1.31, 1.31, 1.35, 1.38, 1.41, 1.43, 1.44, 1.47, 1.47, 1.48, 1.50

Step2: Use the percentile formula

The formula for the percentile $P$ of a value $x$ in a data - set of size $n$ is $L=\frac{k}{100}\times n$, where $k$ is the percentile we want to find and $n$ is the number of data points. Here, $n = 50$. We want to find the percentile of the value $x = 1.10$. First, count the number of values less than or equal to 1.10. There are 21 values less than or equal to 1.10.
The percentile $P$ is calculated as $P=\frac{\text{number of values less than or equal to }x}{n}\times100$. Substituting the values, we have $P=\frac{21}{50}\times100$.

Step3: Calculate the percentile

$P=\frac{21}{50}\times100 = 42$

Answer:

42