Question

use the accompanying radiation levels (in w/kg) for 50 different cell phones. find the percentile corresponding to 0.60 w/kg. the percentile corresponding to 0.60 w/kg is (round to the nearest whole number as needed.) radiation levels 0.19 0.23 0.29 0.48 0.56 0.57 0.60 0.62 0.74 0.83 0.88 0.88 0.90 0.90 0.92 0.94 0.94 1.00 1.06 1.11 1.11 1.11 1.13 1.13 1.14 1.14 1.15 1.16 1.17 1.18 1.19 1.24 1.25 1.26 1.27 1.28 1.29 1.31 1.32 1.32 1.33 1.36 1.41 1.42 1.43 1.46 1.47 1.48 1.54 1.55

Explanation:

Step1: Sort the data

The data is already sorted in ascending - order as given: 0.19, 0.23, 0.29, 0.48, 0.56, 0.57, 0.60, 0.62, 0.74, 0.83, 0.88, 0.88, 0.90, 0.90, 0.92, 0.94, 0.94, 1.00, 1.06, 1.11, 1.11, 1.11, 1.13, 1.13, 1.14, 1.14, 1.15, 1.16, 1.17, 1.18, 1.19, 1.24, 1.25, 1.26, 1.27, 1.28, 1.29, 1.31, 1.32, 1.32, 1.33, 1.36, 1.41, 1.42, 1.43, 1.46, 1.47, 1.48, 1.54, 1.55

Step2: Use the percentile formula

The formula for the percentile \(P\) of a value \(x\) in a data - set of size \(n\) is \(L=\frac{k}{100}(n + 1)\), where \(k\) is the percentile we want to find and \(n\) is the number of data points. Here, \(n = 50\). To find the percentile of \(x = 0.60\), we first count the number of values less than or equal to \(0.60\). There are 7 values less than or equal to \(0.60\).
The percentile \(P\) is calculated as \(P=\frac{\text{number of values less than or equal to }x}{n}\times100\). Substituting the values, we get \(P=\frac{7}{50}\times100 = 14\)

Answer:

14