Q.12 - The Practice of Statistics for AP

Question

Tall girls Refer to Exercise 10. 

(a) Make a graph of the population distribution. 

(b) Sketch a possible graph of the distribution of sample data for the SRS of size $20$ taken by the AP Statistics class. 

Step-by-Step Solution

Answer

a). A graph of the population distribution is 

b). A possible graph of the distribution of sample data is

Part (a) Step 1: Given Information

Tall girls:

Part (a) Step 2: Explanation

The population distribution is given to be $\mathrm{N}(64,2.5)$, which means a normal distribution with mean $64$ and standard deviation $2.5$.

$\mu =64$

$\sigma =2.5$

A general normal distribution with mean $\mu$ and standard deviation $\sigma$ is of the form:

Part (a) Step 3: Explanation

The graph of the population distribution is 

Part (b) Step 1: Given Information

Tall girls:

$20$ individuals are in the sample

We also know that approximately

$\mu =64$

$\sigma =2.5$

Part (b) Step 2: Explanation

The width of all bars should be equal and the height should be equal to the number of students.

The bars should be roughly centered about $64$and the range of values should be within $2$ standard deviations of the mean.

Part (b) Step 3: Explanation

Dot plot:

Draw a number line and place dots above the corresponding numbers which should be centered at about $64$ and the range of values should be within $2$ standard deviations of the mean.