Question

use the accompanying radiation levels (in \\(\frac{w}{kg}\\)) for 50 different cell phones. find the percentile corresponding to 0.50 \\(\frac{w}{kg}). the percentile corresponding to 0.50 \\(\frac{w}{kg}) is . (round to the nearest whole number as needed.) radiation levels: 0.19 0.23 0.34 0.50 0.60 0.62 0.64 0.64 0.71 0.87 0.88 0.88 0.94 0.94 0.94 0.99 1.01 1.03 1.06 1.08 1.09 1.09 1.11 1.12 1.12 1.14 1.17 1.18 1.19 1.22 1.22 1.25 1.20 1.20 1.27 1.27 1.30 1.31 1.32 1.32 1.33 1.34 1.35 1.37 1.41 1.45 1.49 1.49 1.54 1.55

Explanation:

Step1: Sort the data

The data is already sorted in the given list of radiation - levels.

Step2: Use the percentile formula

The formula for the position of the $p$th percentile in a data - set of size $n$ is $L=\frac{p}{100}\times n$. Here, $p$ is the percentile we want to find and $n$ is the number of data points. Given $p$ (the percentile we want to find) and $n = 50$. For the $p$th percentile, $L=\frac{p}{100}\times n$. We want to find the percentile corresponding to a value, but we can also use the position formula. Let's assume we want to find the position of the value $0.50$. First, count the number of values less than or equal to $0.50$. There are 4 values ($0.19,0.23,0.34,0.50$) less than or equal to $0.50$.
The formula for the percentile $P$ is $P=\frac{\text{number of values less than or equal to the value}}{\text{total number of values}}\times100$. So $P=\frac{4}{50}\times100 = 8$.

Answer:

8