The proportion of individuals insured by the All-Driver Automobile Insurance Company who received at least one traffic ticket during a five-year period is 0.15. (a) Show the sampling distribution of p if a random sample of 180 insured individuals is used to estimate the proportion having received at least one ticket.

A sign in the elevator of a college library 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 at this college is 155 pounds, that the standard deviation is 27 pounds, and that the distribution of weights of individuals on campus is approximately normal. A random sample of 16 persons from the campus will be selected. (a) What is the mean of the sampling distribution of  x? μx =  (b) What is the standard deviation of the sampling distribution of  x? σx =   (c) What average weights (in pounds) for a sample of 16 people will result in the total weight exceeding the weight limit of 2,500 pounds? The average weight of 16 persons needs to be greater than   lbs to exceed the weight limit of the elevator. (d) 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.)

The Institute for College Access and Success reported that 67% of college students in 2008 graduated with student loan debt. A random sample of 85 graduates is drawn. a) Find the mean of the sampling distribution. b) Find the standard deviation of the sampling distribution. c) Find the probability that less than 60% of the people in the sample were in debt. d) Find the probability that more than 75% of the people in the sample were in debt.

The proportion of students at a large high school who live within five miles of the school is p = 0.19. The principal takes a random sample of 17 students from this school. Which is the best description of the shape for the sampling distribution of  ? The sampling distribution of  is approximately Normal because  . Because  , the sampling distribution of  is not approximately Normal. The sampling distribution of  is skewed left and centered at 0.81. Because , the sampling distribution of  is not approximately Normal. Because p = 0.19 is closer to 0 than 1, the sampling distribution of  is skewed to the left. Because , the sampling distribution of  is not approximately Normal. Because p = 0.19 is closer to 0 than 1, the sampling distribution of  is skewed to the right.