Concept explainers
Whether the distribution of the percent of state residents who are age 65 and older approximately Normal.
Answer to Problem R2.8RE
Yes, the distribution of the percent of state residents who are age 65 and older approximately Normal.
Explanation of Solution
Given information:
According to 68 − 95 − 99.7 rule:
68% of the data of a
95% of the data of a normal distribution lies with 2 standard deviation from the mean.
99.7% of the data of a normal distribution lies with 1 standard deviation from the mean.
Then
The general Normal density graph is represented as:
Note that
The sample has 40 out of 51 observations within 1 standard deviation of the mean.
That means
The sample has 78.43% observations within 1 standard deviation.
Between
And
Also note that
The sample has 48 out of 51 observations within 2 standard deviation of the mean.
That means
The sample has 94.12% observations within 2 standard deviation.
Between
And
Also note that
The sample has 50 out of 51 observations within 3 standard deviation of the mean.
That means
The sample has 98.04% observations within 3 standard deviation.
Between
And
We have that
78.43% is close to 68%.
94.12% is close to 95%.
98.04% is very close to 99.7%.
This implies
The data reasonably follows 68 − 95 − 99.7 rule.
Thus,
The distribution is approximately Normal.
Chapter 2 Solutions
PRACTICE OF STATISTICS F/AP EXAM
Additional Math Textbook Solutions
Essentials of Statistics (6th Edition)
STATS:DATA+MODELS-W/DVD
Fundamentals of Statistics (5th Edition)
Elementary Statistics: Picturing the World (6th Edition)
Statistics for Business and Economics (13th Edition)
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