Chapter 7.1, Problem 12E

(a)

To determine

To construct: a graph of the population distribution.

Explanation of Solution

Calculation:

  $\begin{array}{l}\mu =64\\ \sigma =2.5\end{array}$

Middle 68% of a normal distribution lies within 1 standard deviation from the mean of the distribution.

Middle 95% of a normal distribution lies within 2 standard deviation from the mean of the distribution.

Middle 99.7% of a normal distribution lies within 3 standard deviation from the mean of the distribution.

The graph of the general Normal density curve is then.

Finding the 1, 2 and 3 standard deviations from the mean

  $\begin{array}{l}\mu -3\sigma =64-3\left(2.5\right)=56.5\\ \mu -2\sigma =64-2\left(2.5\right)=59\\ \mu -\sigma =64-2.5=61.5\\ \mu +\sigma =64+2.5=66.5\\ \mu +2\sigma =64+2\left(2.5\right)=69\\ \mu +3\sigma =64+3\left(2.5\right)=71.5\end{array}$

Graph:

  

  

(b)

To determine

To construct: a dot plot of the distribution of sample data.

Explanation of Solution

Graph:

  

Mean $\mu =64$ inches and

Standard deviation $\sigma =2.5$ inches

It is expected that the simple random sample (SRS) size 20 to have 20 data values that are centred approximately 64, where all data values are predict to be between $\mu -3\sigma =64-3\left(2.5\right)=56.5$ and $\mu +3\sigma =64+3\left(2.5\right)=71.5$

Moreover, the pattern in the 20 dots of the dot plot should form roughly a bell-shaped pattern.