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.) radiation levels 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

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 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 \(L\) is the locator. First, count the number of data points \(n = 50\). Then, count the number of values less than or equal to \(1.10\). There are 29 values less than or equal to \(1.10\) in the data - set.
The formula for the percentile of a value \(x\) is \(P=\frac{\text{number of values less than or equal to }x}{n}\times100\).
Substitute the number of values less than or equal to \(1.10\) (which is 29) and \(n = 50\) into the formula: \(P=\frac{29}{50}\times100\).

Step3: Calculate the percentile

\(P=\frac{29}{50}\times100=58\).

Answer:

58