Chapter 11.10, Problem 15PPSE

Solution

To find: To find the percent of data from 42 to 58.

The percent of data from 42 to 58 is 68%

Given information:

Given, a set of data has a normal distribution with a mean of 50 and a standard deviation of 8.

Calculation:

One standard deviation below and above the mean are:

  $\begin{array}{l}50-8=42\\ 50+8=58\end{array}$

Two standard deviation below and above the mean are:

  $\begin{array}{l}50-2\left(8\right)=34\\ 50+2\left(8\right)=66\end{array}$

In a normal distribution, the data is distributed equally i.e., 50% on either side of the mean.

The data within the first standard deviation contains 34% of data on each side.

The data between the first standard deviation and second standard deviation contains 13.5% of data on each side.

The data between the second standard deviation and third standard deviation contains 2.35% of data on each side.

Here, 42 and 58 are the bounds of first standard deviation on either side.

Hence the percent of data from 42 to 58 is given by:

  $\begin{array}{l}p\approx 34+34\\ p\approx 68\%\end{array}$

Conclusion:

The percent of data from 42 to 58 is 68%