A headline in USA Today states that “most stay at first job less than 2 years.” That headline is based on an Experience.com poll of 320 college graduates. Among those polled, 78% stayed at their first full-time job less than 2 years.

a. Assuming that 50% is the true percentage of graduates who stay at their first job less than two years, find the mean and standard deviation of the numbers of such graduates in randomly selected groups of 320 graduates.

b. Assuming that the 50% rate in part (a) is correct, find the range of usual values for the numbers of graduates among 320 who stay at their first job less than two years.

c. Find the actual number of surveyed graduates who stayed at their first job less than two years. Use the range of values from part (b) to determine whether that number is unusual. Does the result suggest that the headline is not justified?

d. This statement was given as part of the description of the survey methods used: “Alumni who opted-in to receive communications from Experience were invited to participate in the online poll, and 320 of them completed the survey.” What does that statement suggest about the results?