Chapter 2.2, Problem 41E

To determine

To plot: a Normal curve where the mean and standard deviation are located.

Answer to Problem 41E

The curve drawn is:

  

Explanation of Solution

Given:

Meanis 69 inches

Standard deviation is 2.5 inches

Calculation:

Empirical rule for normal distribution

Approximately 68% of the observations are within 1 standard deviation of the mean.

  $\begin{array}{l}\overline{x}-s=69-2.5=66.5\\ \overline{x}+s=69+2.5=71.5\end{array}$

Approximately 95% of the observations are within 2 standard deviations ofthe mean.

  $\begin{array}{l}\overline{x}-2s=69-2\left(2.5\right)=64\\ \overline{x}+2s=69+2\left(2.5\right)=71.5\end{array}$

Approximately 99.7% of the observations are within 3 standard deviations ofthe mean.

  $\begin{array}{l}\overline{x}-3s=69-3\left(2.5\right)=61.5\\ \overline{x}+3s=69+3\left(2.5\right)=76.5\end{array}$

Using this information, we can then draw the sketch of the distribution of the men’s heights:

  

Conclusion:

Thus, the curve is drawn.