SKILL BUILDER 7: THE 95% RULE In Exercises 2.118 to 2.121, use the 95% rule and the fact that the summary statistics come from a dis- tribution that is symmetric and bell-shaped to find an interval that is expected to contain about 95% of the data values. 2.118 A bell-shaped distribution with mean 200 and standard deviation 25. 2.119 A bell-shaped distribution with mean 10 and standard deviation 3. 2.120 A bell-shaped distribution with mean 1000 and standard deviation 10. 2.121 A bell-shaped distribution with mean 1500 and standard deviation 300. 2.122 Estimating Summary Statistics For the data- set
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98
CHAPTER 2 Describing Data
SKILL BUILDER 7: THE 95% RULE
In Exercises 2.118 to 2.121, use the 95% rule and
the fact that the summary statistics come from a dis-
tribution that is symmetric and bell-shaped to find
an interval that is expected to contain about 95% of
the data values.
2.118 A bell-shaped distribution with mean 200
and standard deviation 25.
2.119 A bell-shaped distribution with mean 10 and
standard deviation 3.
2.120 A bell-shaped distribution with mean 1000
and standard deviation 10.
2.121 A bell-shaped distribution with mean 1500
and standard deviation 300.
2.122 Estimating Summary Statistics For the data-
set
45, 46, 48, 49, 49, 50, 50, 52, 52, 54, 57, 57, 58, 58, 60, 61
(a) Without doing any calculations, estimate which
of the following numbers is closest to the
mean:
60
52
17
50](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9ceadcea-1d0c-46b9-af7a-48f9b0bf3d90%2Fb74de2d4-3b0f-4b07-bb58-f12192d47ac7%2Fp7byaku_processed.jpeg&w=3840&q=75)
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Introduction: The top of the graph, which provides a symbolic image of the average, median, and mode for a normal distribution, will possess the same score. Because the cumulative distribution graph of the normal distribution resembles a bell, it is generally referred to simply as the bell curve. When using various statistical methods data and arriving at conclusions, it is beneficial to have a symmetrical distribution. In the given scenario, we need to find the 95% of data distribution for the given normally distributed data. The mean and standard deviation were provided for finding the 95% area of the distributions.
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