Question

In Exercises 17–20, use the following cell phone airport data speeds (Mbps) from Sprint. Find the percentile corresponding to the given data speed.

0.2 0.3 0.3 0.3 0.3 0.3 0.3 0.4 0.4 0.4 0.5 0.5 0.5 0.5 0.5 0.6 0.6 0.7 0.8 1.0 1.1 1.1 1.2 1.2 1.6 1.6 2.1 2.1 2.3 2.4 2.5 2.7 2.7 2.7 3.2 3.4 3.6 3.8 4.0 4.0 5.0 5.6 8.2 9.6 10.6 13.0 14.1 15.1 15.2 30.4

9.6 Mbps

Short answer

The speed of 9.6 Mbps corresponds to the 86^th percentile.

Step-by-step solution

Given information 

The sample provided has a group of 50 data speeds.

Explain percentile  

The percentileof a given value involves calculating the ratio of the number of values less than that given value to the total number of values.

The ratio of two values is multiplied by 100 to obtain the percentile. In terms of a mathematical expression, it is written as follows:

$P_x=\frac{Numberofvaluesbelowx}{Totalnumberofvalues}\times 100$

Compute the percentile corresponding to 9.6 Mbps

Steps to find the percentile value:

• List the values from the smallest to the largest.
• Enumerate the total number of observations.
• Enumerate the number of observations less than 9.6 Mbps.
• Use the formula mentioned above to calculate the percentile.

The percentile corresponding to a data speed of 9.6 Mbps is as follows:

$$\begin{gathered} P_{9.6}=\frac{Numberofvaluesbelow9.6}{Totalnumberofvalues}\times 100 \\ =\frac{43}{50}\times 100 \\ =86 \end{gathered}$$

Therefore, 9.6 Mbps corresponds to the 86^th percentile.