Question

1.) In the library on a university campus, there is a sign in the elevator that indicates a limit of 16 persons. In addition, there is a weight limit of 2,500 pounds. Assume that the average weight of students, faculty, and staff on campus is 155 pounds, that the standard deviation is 27 pounds, and that the distribution of weights of individuals on campus is approximately normal. Suppose a random sample of 16 persons from the campus will be selected.

a. What is the standard deviation of the sampling distribution of x bar?

b. What mean weights (in pounds) for a sample of 16 people will result in the total weight exceeding the weight limit of 2,500 pounds? The mean weight of 16 persons needs to be greater than _____lbs to exceed the weight limit of the elevator.

c. What is the probability that a random sample of 16 people will exceed the weight limit? (Use a table or technology. Round your answer to four decimal places.)

2. In a survey of 485 potential jurors, one study found that 340 were regular watchers of at least one crime-scene forensics television series. Assuming that it is reasonable to regard this sample of 485 potential jurors as representative of potential jurors in the United States, use the given information to construct a 95% confidence interval for the true proportion of potential jurors who regularly watch at least one crime-scene investigation series. (Use Table 3 in Appendix A. Give the answer to three decimal places.) ( ______, ________) please in this form.

3. In a survey of 1000 randomly selected adults in the United States, participants were asked what their most favorite and what their least favorite subject was when they were in school (Associated Press, August 17, 2005). In what might seem like a contradiction, math was chosen more often than any other subject in both categories! Math was chosen by 224 of the 1000 as the favorite subject, and it was also chosen by 366 of the 1000 as the least favorite subject.

(_____, .2498)

4. Many consumers pay careful attention to stated nutritional contents on packaged foods when making purchases. It is therefore important that the information on packages be accurate. A random sample of n = 12 frozen dinners of a certain type was selected from production during a particular period, and the calorie content of each one was determined. (This determination entails destroying the product, so a census would certainly not be desirable!) Here are the resulting observations, along with a boxplot and normal probability plot

the values are

255	244	239	242	265	245	259	248
225	226	251	233

a. Carry out a formal test of the hypotheses suggested in part (b). (Use Table 4 in Appendix A. Use α = 0.05. Round your test statistic to two decimal places and your P-value to three decimal places.)

t= ___

df= 11

P= ___

please answer all parts, i appreciate it.

Answer 1

( 2 )

95% confidence interval = ( 0.660 , 0.742 )