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(a)
To draw:
The graph of a curve that represents the frequency distribution.
(a)
Explanation of Solution
Given:
Standard deviation =1.5
Concept used:
Normal distribution: - A normal distribution is a frequency distribution that often occurs
There is a large number of values in a set of data.
The graph of this distribution is a symmetric, bell-shaped curve.
Calculation:
Normally distributed data is =12
Standard deviation =1.5
σ=1.5
Draw the graph of the frequency distribution
The frequency and probability distribution are identically shaped for a normally distributed data set.
This graph is bell curve centered at the mean /median /mode and symmetric about this point.
(b)
To find:
The interval about the mean that includes 68.3% of the data.
(b)
Answer to Problem 9E
(10.5,13.5)
Explanation of Solution
Given:
Normally distributed data is =12
Standard deviation =1.5
Concept used:
Standard deviation of a set is falls within the interval of
(m−σ,m+σ)
Calculation:
Normally distributed data is =12
Standard deviation =1.5
σ=35
68.3% Standard deviation of a set is falls within the interval of
(m−σ,m+σ) ..................(1)
Using standard deviation in equation (1)
=(m−σ,m+σ)=(10.5,13.5)
The interval about the mean that includes 68.3% of the data is (10.5,13.5)
(c)
To find:
The data is between 7.5 and 16.5 .
(c)
Answer to Problem 9E
88.7%
Explanation of Solution
Given:
Normally distributed data is =12
Standard deviation =1.5
Concept used:
Normal distribution: - A normal distribution is a frequency distribution that often occurs
There is a large number of values in a set of data.
The graph of this distribution is a symmetric, bell-shaped curve.
Calculation:
Normally distributed data is =12
Standard deviation =1.5
σ=1.5
Each of the limits in terms of the mean
12−7.5=4.516.5−12=4.5
Using the formula
ˉX±tσ=12±4.5tσ=3.5t(1.5)=4.5t=4.51.5t=3
t=3→88.7%
The values lie between 7.5 and 16.5 is 88.7% .
(d)
To find:
The data is between 9 and 15 .
(d)
Answer to Problem 9E
95.5%
Explanation of Solution
Given:
Normally distributed data is =12
Standard deviation =1.5
Concept used:
Normal distribution: - A normal distribution is a frequency distribution that often occurs
There is a large number of values in a set of data.
The graph of this distribution is a symmetric, bell-shaped curve.
Calculation:
Normally distributed data is =12
Standard deviation =1.5
σ=1.5
Each of the limits in terms of the mean
12−9=315−12=3
Using the formula
ˉX±tσ=12±3tσ=3t(1.5)=3t=31.5t=2
t=2→95.5%
The values lie between 7.5 and 16.5 is 95.5% .
Chapter 14 Solutions
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