Chapter 11.10, Problem 3LC

Solution

To find: To find the percent of scores are between 85 and 95.

The percent of scores are between 85 and 95 is 47.5%

Given information:

Given,the scores on an exam are normally distributed, with a mean of 85 and a standard deviation of 5.

Calculation:

One standard deviation below and above the mean are:

  $\begin{array}{l}85-5=80\\ 85+5=90\end{array}$

Two standard deviation below and above the mean are:

  $\begin{array}{l}85-2\left(5\right)=75\\ 85+2\left(5\right)=95\end{array}$

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, 85 is the mean and 95is the second standard deviation on the right.

Hence the percent of scores between 85 and 95 is given by:

  $\begin{array}{l}p\approx 34+13.5\\ p\approx 47.5\%\end{array}$

Conclusion:

The percent of scores are between 85 and 95 is 47.5%