1. The distribution of scores on a recent test closely followed a Normal Distribution with a mean of 22 points and a standard deviation of 2 points. For this question, DO NOT apply the standard deviation rule.

(a) What proportion of the students scored at least 24 points on this test, rounded to five decimal places?

(b) What is the 23 percentile of the distribution of test scores, rounded to three decimal places?

2. Same-sex marriage: In a recent ABC News/Washington Post poll, 1296 adults nationwide answered the question, "Overall, do you support or oppose allowing gays and lesbians to marry legally?"

Of the respondents, 452 support same-sex marriage. What is the 95% confidence interval for the proportion of all American adults who support same-sex marriage?

http://www.washingtonpost.com/page/2010-2019/WashingtonPost/2015/04/23/National-Politics/Polling/release_395.xml

1. (0.323, 0.375)
2. (0.336, 0.362)
3. (0.327, 0.371)
4. (0.315, 0.383)

3. In 2015 as part of the General Social Survey, 1125 randomly selected American adults responded to this question:

"Some countries are doing more to protect the environment than other countries. In general, do you think that America is doing more than enough, about the right amount, or too little?"

Of the respondents, 514 replied that America is doing about the right amount. What is the 95% confidence interval for the proportion of all American adults who feel that America is doing about the right amount to protect the environment.

1. (0.442, 0.472)
2. (0.419, 0.495)
3. (0.432, 0.481)
4. (0.428, 0.486)

4. The ability to find a job after graduation is very important to GSU students as it is to the students at most colleges and universities.

Suppose we take a poll (random sample) of 3891 students classified as Juniors and find that 2867 of them believe that they will find a job immediately after graduation.

What is the99% confidence interval for the proportion of GSU Juniors who believe that they will, immediately, be employed after graduation.

1. (0.719, 0.755)
2. (0.73, 0.744)
3. (0.723, 0.751)
4. (0.725, 0.748)

5. Two different groups in a statistics class are conducting a survey to estimate the mean number of units students at their college are enrolled in. The population mean and standard deviation are unknown. The sample from the first group survey has 49 data values. The sample from the second group survey has 81 data values. For each sample, the groups construct a 90% confidence interval to estimate the population mean.

Which confidence interval will have greater precision (smaller width) for estimating the population mean?

1. The confidence interval based on the sample of 49 data values will be more precise.
2. Both confidence intervals will have the same precision.
3. The confidence interval based on the sample of 81 data values will be more precise.

6. A group of engineers developed a new design for a steel cable. They need to estimate the amount of weight the cable can hold. The weight limit will be reported on cable packaging. The engineers take a random sample of 41 cables and apply weights to each of them until they break. The 41 cables have a mean breaking weight of 772.3 lb. The standard deviation of the breaking weight for the sample is 15.3 lb.

Find the 95% confidence interval to estimate the mean breaking weight for this type cable.

( , )

Your answer should be to 2 decimal places.

7. According to the website www.collegedrinkingprevention.gov, "About 25 percent of college students report academic consequences of their drinking including missing class, falling behind, doing poorly on exams or papers, and receiving lower grades overall." A statistics student is curious about drinking habits of students at his college. He wants to estimate the mean number of alcoholic drinks consumed each week by students at his college. He plans to use a 90% confidence interval. He surveys a random sample of 65 students. The sample mean is 3.91 alcoholic drinks per week. The sample standard deviation is 3.49 drinks.

Construct the 90% confidence interval to estimate the average number of alcoholic drinks consumed each week by students at this college.

( , )

Your answer should be rounded to 2 decimal places.

8. According to the website www.collegedrinkingprevention.gov, "About 25 percent of college students report academic consequences of their drinking including missing class, falling behind, doing poorly on exams or papers, and receiving lower grades overall." A statistics student is curious about drinking habits of students at his college. He wants to estimate the mean number of alcoholic drinks consumed each week by students at his college. He plans to use a 95% confidence interval. He surveys a random sample of 57 students. The sample mean is 3.79 alcoholic drinks per week. The sample standard deviation is 3.61 drinks.

Construct the 95% confidence interval to estimate the average number of alcoholic drinks consumed each week by students at this college.

( , )

Your answer should be rounded to 2 decimal places.

9. According to the website www.collegedrinkingprevention.gov, "About 25 percent of college students report academic consequences of their drinking including missing class, falling behind, doing poorly on exams or papers, and receiving lower grades overall." A statistics student is curious about drinking habits of students at his college. He wants to estimate the mean number of alcoholic drinks consumed each week by students at his college. He plans to use a 95% confidence interval. He surveys a random sample of 57 students. The sample mean is 3.79 alcoholic drinks per week. The sample standard deviation is 3.61 drinks.

Construct the 95% confidence interval to estimate the average number of alcoholic drinks consumed each week by students at this college.

( , )

Your answer should be rounded to 2 decimal places.

10. According to the website www.collegedrinkingprevention.gov, "About 25 percent of college students report academic consequences of their drinking including missing class, falling behind, doing poorly on exams or papers, and receiving lower grades overall." A statistics student is curious about drinking habits of students at his college. He wants to estimate the mean number of alcoholic drinks consumed each week by students at his college. He plans to use a 99% confidence interval. He surveys a random sample of 49 students. The sample mean is 3.92 alcoholic drinks per week. The sample standard deviation is 3.33 drinks.

Construct the 99% confidence interval to estimate the average number of alcoholic drinks consumed each week by students at this college.

( , )

Your answer should be rounded to 2 decimal places.