Chapter 7.1, Problem 12E

(a)

To determine

To graph: The population distribution.

Explanation of Solution

Given information:

Mean, $\mu =64$ inches

Standard deviation, $\sigma =2.5$ inches

Number of 16-year old females = 300

Number of 16-year old females for SRS = 20

The population distribution = $N\left(64,2.5\right)$

The dotplot:

  

Given that the population distribution is $N\left(64,2.5\right)$ .

This means that the mean and standard deviation of the normal distribution are 64 and 2.5 respectively.

So, $\mu =64$ and $\sigma =2.5$

The required graph of the population distribution can be drawn by using the general form of normal distribution whose mean is $\mu$ and standard deviation is $\sigma$ .

Thus, the required graph is shown below:

  

(b)

To determine

To graph: The distribution of sample data for the SRS of size 20 taken by the AP Statistics class.

Explanation of Solution

Given information:

Mean, $\mu =64$ inches

Standard deviation, $\sigma =2.5$ inches

Number of 16-year old females = 300

Number of 16-year old females for SRS = 20

The population distribution = $N\left(64,2.5\right)$

The dotplot:

  

Given that the number of females for the SRS is 20.

Also, the population distribution is $N\left(64,2.5\right)$ .

This means that the mean and standard deviation of the normal distribution are 64 and 2.5 respectively.

So, $\mu =64$ and $\sigma =2.5$

The histogram of the given data is shown below:

  

In the above histogram, widths of the bars are equal and the heights of the bars are the number of students. The bars in the histogram are roughly centered about 64 and the ranges of values are between 2 standard deviations of the mean.

The dotplot of the given data is shown below:

  

The dots in the dotplot are roughly centered about 64 and the ranges of values are between 2 standard deviations of the mean.