Explore BrainMass
Share

Normal Distribution

This content was STOLEN from BrainMass.com - View the original, and get the already-completed solution here!

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.

© BrainMass Inc. brainmass.com October 24, 2018, 5:57 pm ad1c9bdddf
https://brainmass.com/statistics/normal-distribution/normal-distribution-26168

Attachments

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.

$2.19
See Also This Related BrainMass Solution

Statistics questions - normal and continuous

1. What are the characteristics of a normal distribution?

2. List some examples of continuous data.

3. What is the name of the distribution that measures the number of occurrences of an event during specified intervals?

4. What would be the characteristics of a binomial distribution?

5. A population consists of ten items, six of which are defective. In a sample of three items, what is the probability that exactly two are defective?

6. A Federal study reported that 7.5 percent of the U.S. workforce has a drug problem. A drug enforcement official for the State of Indiana wished to investigate this statement. In his sample of 20 employed workers:
a. How many would you expect to have a drug problem? What is the standard deviation?
b. What is the likelihood that none of the workers sampled has a drug problem?
c. What is the likelihood at least one has a drug problem?

7. What is "Bias"?

8. What is the Central Limit Theorem? What does it imply?

9. What is sampling error? How is it calculated?

10. What are the three measures of central tendency?

View Full Posting Details