Chapter 3.2, Problem 3.24E

To determine

To estimate the mean and standard deviation from the given graph.

Answer to Problem 3.24E

Mean = 10

Standard deviation = 2

Explanation of Solution

Given:

  

Concept used:

The mean of a normal distribution falls at the center of the distribution, the most of the data of a normal distribution falls with 3 standard deviations from the mean.

Calculation:

Based on the concept mentioned above, the mean of the given normal distribution is 10, the entire data is distributed from 4 to 16 and the as per the concept the whole data is distributed with 6 standard deviations.

  $\begin{array}{c}6\sigma =16-4\\ =\frac{12}{6}\\ =2\end{array}$

The approximate value of mean is 10 and the standard deviation is 2.