Concept explainers
(a)
To describe: the shape, center, and spread of the distribution of shark lengths
(a)
Answer to Problem 63E
Shape: symmetric and roughly bell-shaped.
Center:
Spread: standard deviation is 2.5499
Explanation of Solution
Given:
18.7 | 12.3 | 18.6 | 16.4 | 15.7 | 18.3 | 14.6 | 15.8 | 14.9 | 17.6 | 12.1 |
16.4 | 16.7 | 17.8 | 16.2 | 12.6 | 17.8 | 13.8 | 12.2 | 15.2 | 14.7 | 12.4 |
13.2 | 15.8 | 14.3 | 16.6 | 9.4 | 18.2 | 13.2 | 13.6 | 15.3 | 16.1 | 13.5 |
19.1 | 16.2 | 22.8 | 16.8 | 13.6 | 131 | 15.7 | 19.7 | 18.7 | 13.2 | 16.8 |
Lengths of sharks are in feet of 44
Calculation:
Variable | N | Mean | St.Dev. | Min | M | Max | ||
Shark length | 44 | 15.586 | 2.550 | 9.40 | 13.525 | 15.75 | 17.40 | 22.80 |
Shark lengths are roughly symmetric with a peak at 16 and vary from minimum value of 9.40 feet to maximum value 22.8 feet.
Shape: symmetric and roughly bell-shaped.
Center: Mean is 15.5884 and median is 15.75
Spread: standard deviation is 2.5499
Conclusion:
Shape: symmetric and roughly bell-shaped.
Center: Mean is 15.5884 and median is 15.75
Spread: standard deviation is 2.5499
(b)
To describe: the percent of observations that fall within one, two, and three standard deviations of the mean.
(b)
Answer to Problem 63E
One standard deviations = 68.2%
Two standard deviations = 95.5%
Three standard deviations = 100%
Explanation of Solution
Calculation:
From the above output,
Mean,
Sample standard deviation,
Percent of interval
Percent of interval
Percent of interval
According to the 68-95-99.7 rule, approximately 68.2% of the data values fall within one standard deviation. 95.5% of the data values fall within two standard deviations, and 100% of the data values fall within three standard deviations of the mean.
Conclusion:
Therefore,
One standard deviations = 68.2%
Two standard deviations = 95.5%
Threestandard deviations = 100%
(c)
To construct: a Normal probability plot and interpret the plot.
(c)
Answer to Problem 63E
The pattern in the Normal probability plot is fairly linear and it is roughly
Explanation of Solution
Calculation:
A Normal probability plot from Minitab is shown below:
The plot is fairly linear except from one small shark and one large shark lengths, indicating that the Normal distribution is appropriate.
Conclusion:
Therefore, a Normal probability plot is plotted. The pattern in the Normal probability plot is fairly linear and it is roughly normally distributed.
(c)
To explain:whether the data are approximately Normal
(c)
Answer to Problem 63E
The data are approximately Normal
Explanation of Solution
Calculation:
Results from the parts (a), (b), and (c) indicates that shark lengths are approximately normal.
Approximately normal, because the normal probability plot was roughlynormal and the histogram were roughly bell-shaped.
Conclusion:
Therefore, the data are approximately Normal
Chapter 2 Solutions
The Practice of Statistics for AP - 4th Edition
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