
(a)
To obtain: The proportion of females aged 20-29 weighted under 100 pounds.
To find: The percent of the
(a)

Answer to Problem 3.51E
The proportion of females aged 20-29 weighted under 100 pounds is 0.0255.
The percent of the
Explanation of Solution
Given info:
The NHANES survey of 2009-2010 includes the weights of 548 females in the United States aged 20-29. The weights of females follow
Calculation:
For proportion of females aged 20-29 weighted under 100 pounds:
The formula to find the proportion of females aged 20-29 weighted under 100 pounds is,
Substitute 14 for ‘number of females aged 20-29 weighted under 100 pounds’ and 548 for ‘Total number of females’.
Thus, the proportion of females aged 20-29 weighted under 100 pounds is 0.0255.
For percent of the
Define the random variable x as weights of the females.
The formula for the standardized score is,
The females aged 20-29 weighted below 100 pounds is denoted as
Subtract the mean and then divide by the standard deviation to transform the value of x into standard normal z.
Where, standardized score
The percent of the
Use Table A: Standard normal cumulative proportions to find the area.
Procedure:
- Locate –1.2 in the left column of the A-2 Table.
- Obtain the value in the corresponding row below 0.06.
That is,
Thus, the percent of the
(b)
To obtain: The proportion of females aged 20-29 weighted over 250 pounds.
To find: The percent of the
(b)

Answer to Problem 3.51E
The proportion of females aged 20-29 weighted over 250 pounds is 0.0602.
The percent of the
Explanation of Solution
Given info:
The NHANES survey of 2009-2010 includes the weights of 548 females in the United States aged 20-29. From the data the number of females aged 20-29 weighted over 250 pounds is 33. The weights of females follow normal distribution with mean 161.58 pounds and standard deviation 48.96 pounds.
Calculation:
For proportion of females aged 20-29 weighted over 250 pounds:
The formula to find the females aged 20-29 weighted over 250 pounds is,
Substitute 33 for ‘number of females aged 20-29 weighted over 250 pounds’ and 548 for ‘Total number of females’.
Thus, the proportion of females aged 20-29 weighted over 250 pounds is 0.0602.
For percent of the
The females aged 20-29 weighted above 250 pounds is denoted as
Subtract the mean and then divide by the standard deviation to transform the value of x into standard normal z.
Where, standardized score
The percent of the
Use Table A: Standard normal cumulative proportions to find the area to the left of 1.81.
Procedure:
- Locate 1.8 in the left column of the A-2 Table.
- Obtain the value in the corresponding row below 0.01.
That is,
The area to the right of 1.81 is,
Thus, the percent of the
(c)
To check: Whether it is a good idea to summarize the distribution of weights by an
(c)

Answer to Problem 3.51E
The idea is not good to summarize the distribution of weights by a
Explanation of Solution
Justification:
The percentage of females aged 20-29 weighted under 100 pounds is 2.55% and the percentage of females aged 20-29 weighted over 250 pounds is 6.02%.
Using normal distribution, the percentage of
Thus, the results suggest that normal distribution not provides a good approximation to the distribution of weights.
Hence, the idea is not good to summarize the distribution of weights by a
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Chapter 3 Solutions
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