Question

7.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 300 college graduates. Among those​ polled, 78% 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

300 graduates.

The mean is____?

The standard deviation is___?

​(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 300 who stay at their first job less than two years.

The numbers of graduates among 300 who stay at their first job less than two years should usually fall between _____and _____

​(Use ascending order. Round to one decimal place as​ needed.)

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.)

A. Since the actual number is inside of the range of usual values found in part​ (b), it is not unusual.

B. Since the actual number is outside of the range of usual values found in part​ (b), it is not unusual.

C. Since the actual number is outside of the range of usual values found in part​ (b), it is unusual.

D. Since the actual number is inside of the range of usual values found in part​ (b), it is unusual

What does the result suggest about the​ headline?

A. The result suggests that the headline is not justified.

B. The result suggests that the headline is justified.

D. The​ statement, "Alumni who​ opted-in to receive communications from the website were invited to participate in the online​ poll, and 300 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 300 respondent is a _____ sample, the results are ____

Answer 1

7)

here mean of distribution=μ=np=		150
and standard deviation σ=sqrt(np(1-p))=		8.6603

b)

minimum usual value =μ-2*σ =		132.68
maximum usual value =μ-2*σ =		167.32

The numbers of graduates among 300 who stay at their first job less than two years should usually fall between 132.7 to 167.3

c)

The actual number of surveyed graduates who stayed at their first job less than two years is =300*0.78=234

C. Since the actual number is outside of the range of usual values found in part​ (b), it is unusual.

c)

B. The result suggests that the headline is justified.

D)

Since the sample of 300 respondent is a convenience sample the result are biased