Question

#9

A headline in a certain newspaper states that "most stay at first job less than 2 years." That headline is based on an online poll of 280 college graduates. Among those polled, 71% stayed at their first full-time job less than 2 years. Complete parts (a) through (d). 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 280 graduates. The mean is graduates. (Do not round.) The standard deviation is graduates (Round to one decimal place as needed ) b. Assuming that the 50% rate in part (a) is correct, find the range of usual values for the numbers of graduates among 280 who stay at their first job less than two years. The numbers of graduates among 280 who stay at their first job less than two years should usually fall between (Use ascending order. Round to one decimal place as needed) and 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? The actual number of surveyed graduates who stayed at their first job less than two years is (Round to the nearest whole number as needed.) (d) Is the actual number of surveyed graduates who stayed at their first job less than two years unusual? O A. Since the actual number is inside of the range of usual values found in part (D), it is unusual. inside of the range of usual values found in part (b), t is not unusual. OC. Since the actual number is outside of the range of usual values found in part (b), it is not unusual. OD. Since the actual number is outside of the range of usual values found in part (b), it is unusual O B. Since the actual number is d. The statement, "Alumni who opted-in to receive communications from the website were invited to participate in the online poll, and 280 of them completed the survey." was given as part of the description of the survey methods used. What does that statement suggest about the results? Since the sample of 280 respondents is a Vsample, the results are Click to select your answer(s). C Tesdn suggests nal the fheau O B. The result suggests that the headli random d. The statement, "Alumni who opted-in to poll, and 280 of them completed the surve statement suggest about the results? n the website were invited to simple random escription of the survey meth voluntary response Since the sample of 280 respondents is a sample, the results are d. The statement, "Alumni who opted-in to receive communications from the website were invited to participate in the online poll, and 280 completed the survey." was given as part of the description of the survey methods used. What does that statement suggest about the resu Since the sample of 280 respondents is a sample, the results are Click to select your answer(s) very questionable accurate

Answer 1

Given n=280, p=0.5

mean=n*p=280*0.5= 140

standard deviation=√n*p*(1-p)

=sqrt(280*0.5*0.5)

= 8.3666
=8.4

b)
range of usual values - within 2 sd of mean
(140 - 2 * 8.4 , 140 + 2* 8.4)
=( 123.2 , 156.8)

c)
actual number = 280 * 0.71 = 198.8 = 199

option D) is correct
outside the range and unsual