Chapter 2.2, Problem 46E

To determine

To estimate: the mean and standard deviation of the normal density curve

Answer to Problem 46E

The mean is 10 and the standard deviation is 2

Explanation of Solution

Given:

  

Calculation:

The mean lies in the middle of the graph.

The standard deviation is the horizontal distance between the graph and the mean, at a height of slightly more than half the height of the graph.

  

Then we note:

The mean is at about 10.

The standard deviation is about 2.

From the graph we can observe that the inflection points are 8 and 12.

Thus, $\mu +\sigma =12$ . Also the peak value in the graph is 10, it represents the mean $\mu =10$ .

Using the below equation we get the standard deviation.

  $\begin{array}{l}\mu +\sigma =12\\ \Rightarrow 10+\sigma =12\\ \Rightarrow \sigma =2\end{array}$

Conclusion:

Thus,the mean is 10 and the standard deviation is 2