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# Normal Distribution

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Question 1
If a normal distribution of empirical scores is converted to a distribution of z scores:
A. The new mean will be zero
B. The new standard deviation will be one
C. Both A and B
D. Neither A and B.

Question 2
Milquetoasts gracious statistics professor at Northwestern announced that he would drop the poorest exam grade for each student. Milquetoast scored 79 on the first exam. The mean was 67 and the standard deviation four. On the second exam, he made 65. The class mean was 70 and the standard deviation 15. On the third exam, the mean was 75 and the standard deviation three. Milquetoast made 51. On which test was Milquetoasts performance poorest?
A. Exam #1.
B. Exam #2.
C. Exam #3.
D. Neither Exam #1, #2 or #3. There is not enough information in the problem to decide.

Question 3
Replacement times for new Ford Taurus GL automobiles are normally distributed with a mean of 7.1 years and a standard deviation of 1.4 years. Find the probability that seven randomly selected Taurus GL automobiles will have a mean replacement time greater than 7.0 years.

Question 4
Among U.S. households, 24% have telephone answering machines. If a telemarketing campaign involves 2,500 households, find the probability that more than 650 have answering machines.

Question 5
As the sample size increases and if the sample standard deviation remains the same, the standard error of the mean will:
A. Increase.
B. Decrease
C. Remain the same.
D. Increase at first, then decrease.
E. Cannot answer without first knowing the sample size.

Question 6
The U.S. Air Force is reviewing its orders for uniforms because it has a surplus of uniforms for tall recruits and a shortage for shorter recruits. Its review involves data for 772 men between the ages of 18 and 24. That sample group has a mean height of 69.7 inches with a standard deviation of 2.8 inches. Use these sample data to find the 99% confidence interval for the mean height of all men between the ages of 18 and 24.

Question 7
Find the margin of error that corresponds to the given values of n (times) and x (successes) and the degree of confidence: n = 1400, x = 420, 95%.

Question 8
A New York Times article about poll results states, "In theory, in 19 cases out of 20, the results from such a poll should differ by no more than one percentage point in either direction from what would have been obtained by interviewing all voters in the United States." Find the sample size suggested by this statement.

Question 9
When 500 college students are randomly selected and surveyed, it is found that 135 of them own personal computers. Find the point estimate of the true proportion of all college students who own personal computers.

Question 10
When 500 college students are randomly selected and surveyed, it is found that 135 of them own personal computers. Find a 95% confidence interval for the true proportion of all college students who own personal computers.

https://brainmass.com/statistics/normal-distribution/normal-distribution-26168

#### Solution Preview

Question 1
If a normal distribution of empirical scores is converted to a distribution of z scores:
A. The new mean will be zero
B. The new standard deviation will be one
C. Both A and B
D. Neither A and B.

Z distribution is the standard normal distribution ~ N[0, 1], which means the new mean will be zero and the new standard deviation will be one, thus choose C.

Question 2
Milquetoasts gracious statistics professor at Northwestern announced that he would drop the poorest exam grade for each student. Milquetoast scored 79 on the first exam. The mean was 67 and the standard deviation 4. On the second exam, he made 65. The class mean was 70 and the standard deviation 15. On the third exam, the mean was 75 and the standard deviation 3. Milquetoast made 51. On which test was Milquetoasts performance poorest?
A. Exam #1.
B. Exam #2.
C. Exam #3.
D. Neither Exam #1, #2 or #3. There is not enough information in the problem to decide.

Z=(X-M)/SD, and the higher z, the better score.
Since the 3rd exam he scored the lowest (lowest X), the mean is the highest (highest M) and the standard deviation lowest (lowest SD), his 3rd performance should be the poorest.

Question 3
Replacement times for new Ford Taurus GL automobiles are ...

#### Solution Summary

Question 1
If a normal distribution of empirical scores is converted to a distribution of z scores:
A. The new mean will be zero
B. The new standard deviation will be one
C. Both A and B
D. Neither A and B.

Question 2
Milquetoasts gracious statistics professor at Northwestern announced that he would drop the poorest exam grade for each student. Milquetoast scored 79 on the first exam. The mean was 67 and the standard deviation four. On the second exam, he made 65. The class mean was 70 and the standard deviation 15. On the third exam, the mean was 75 and the standard deviation three. Milquetoast made 51. On which test was Milquetoasts performance poorest?
A. Exam #1.
B. Exam #2.
C. Exam #3.
D. Neither Exam #1, #2 or #3. There is not enough information in the problem to decide.

Question 3
Replacement times for new Ford Taurus GL automobiles are normally distributed with a mean of 7.1 years and a standard deviation of 1.4 years. Find the probability that seven randomly selected Taurus GL automobiles will have a mean replacement time greater than 7.0 years.

Question 4
Among U.S. households, 24% have telephone answering machines. If a telemarketing campaign involves 2,500 households, find the probability that more than 650 have answering machines.

Question 5
As the sample size increases and if the sample standard deviation remains the same, the standard error of the mean will:
A. Increase.
B. Decrease
C. Remain the same.
D. Increase at first, then decrease.
E. Cannot answer without first knowing the sample size.

Question 6
The U.S. Air Force is reviewing its orders for uniforms because it has a surplus of uniforms for tall recruits and a shortage for shorter recruits. Its review involves data for 772 men between the ages of 18 and 24. That sample group has a mean height of 69.7 inches with a standard deviation of 2.8 inches. Use these sample data to find the 99% confidence interval for the mean height of all men between the ages of 18 and 24.

Question 7
Find the margin of error that corresponds to the given values of n (times) and x (successes) and the degree of confidence: n = 1400, x = 420, 95%.

Question 8
A New York Times article about poll results states, "In theory, in 19 cases out of 20, the results from such a poll should differ by no more than one percentage point in either direction from what would have been obtained by interviewing all voters in the United States." Find the sample size suggested by this statement.

Question 9
When 500 college students are randomly selected and surveyed, it is found that 135 of them own personal computers. Find the point estimate of the true proportion of all college students who own personal computers.

Question 10
When 500 college students are randomly selected and surveyed, it is found that 135 of them own personal computers. Find a 95% confidence interval for the true proportion of all college students who own personal computers.

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