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Concept explainers
(a)
To find: the shape, center, and spread of the distribution of density measurements.
(a)
![Check Mark](/static/check-mark.png)
Answer to Problem 64E
Shape: the distribution is roughly symmetric
The center 5.4479 (
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 find: the percent of observations that fall within one, two, and three standard deviations of the mean
(b)
![Check Mark](/static/check-mark.png)
Answer to Problem 64E
One standard deviations =
Two standard deviations = 96.55%
Three standard deviations = 100%
Explanation of Solution
The densities follow the
Conclusion:
Therefore,
One standard deviations =
Two standard deviations = 96.55%
Three standard deviations = 100%
(b)
To find: To construct: a Normal probability plot and interpret the plot.
(b)
![Check Mark](/static/check-mark.png)
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 explain: whether the data are approximately Normal
(b)
![Check Mark](/static/check-mark.png)
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.
Chapter 2 Solutions
The Practice of Statistics for AP - 4th Edition
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