Chapter 2.2, Problem 64E

(a)

To determine

To find: the shape, center, and spread of the distribution of density measurements.

Answer to Problem 64E

Shape: the distribution is roughly symmetric

The center 5.4479 (mean) or 5.46(median)

Spread: 0.2209 (standard deviation)

Explanation of Solution

Given:

5.50	5.61	4.88	5.07	5.26	5.55	5.36	5.29	5.58	5.65
5.57	5.53	5.62	5.29	5.44	5.34	5.79	5.10	5.27	5.39
5.42	5.47	5.63	5.34	5.46	5.30	5.75	5.68	5.85

Calculation:

Descriptive statistics and a histogram are provided below:

Descriptive Statistics: earth density

Variable	Mean	StDev	Minimum	Q1	Median	Q3	Maximum
earth density	5.4479	0.2209	4.8800	5.2950	5.4600	5.6150	5.8500

  

The measurements of the earth's density are roughly symmetric with a mean of 5.45 and vary from 4.88 to 5.85.

Shape: the distribution is roughly symmetric (part of the graph is a rough mirror image of the other part of the graph.)

The center is about 5.4479 (mean) or 5.46(median)

Spread is about 0.2209 (standard deviation)

Conclusion:

Therefore,

Shape: the distribution is roughly symmetric

The center 5.4479 (mean) or 5.46(median)

Spread: 0.2209 (standard deviation)

(b)

To determine

To find: the percent of observations that fall within one, two, and three standard deviations of the mean

Answer to Problem 64E

One standard deviations = $-75.86\%$

Two standard deviations = 96.55%

Three standard deviations = 100%

Explanation of Solution

The densities follow the 68-95-99.7 rule closely $-75.86\%$ (22 out of 29) of the densities fall within one standard deviation of the mean. 96.55% (28 out of 29) of the densities fall within two standard deviations of the mean, and 100% of the densities fall within 3 standard deviations of the mean.

Conclusion:

Therefore,

One standard deviations = $-75.86\%$

Two standard deviations = 96.55%

Three standard deviations = 100%

(b)

To determine

To find: To construct: a Normal probability plot and interpret the plot.

Answer to Problem 64E

  

Explanation of Solution

Calculation:

A Normal probability plot from Minitab is shown below:

  

The Normal probability plot is roughly linear, indicating that the densities are approximately Normal.

Conclusion:

Therefore, a Normal probability plot is plotted.

(b)

To determine

To explain: whether the data are approximately Normal

Answer to Problem 64E

the data are approximately Normal

Explanation of Solution

Calculation:

The graphical display in (A), check of the 68-95-99.7 rule in (B), and Normal probability plot in (C) indicate that these measurements are approximately Normal.

Conclusion:

Normal probability plot in (C) indicate that these measurements are approximately Normal.