A headline in a certain newspaper states that \"most stay at first job ess than

Question

A headline in a certain newspaper states that "most stay at first job ess than 2 years. That headline is based on an online pol of 370 o ege graduates. Among those polled 85% stayed at their fist ful-t me oble s tan 2 years compe e a s (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 370 graduates. The mean is 185 graduates. (Simplify your answer.,) The standard deviation is 9.6 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 370 who stay at their first ob less than two years. The numbers of graduates among 370 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.)

Explanation / Answer

Solution:

a. The mean is 195 graduates.

= np

= (370)(0.50)

= 185

The standard deviation is 9.6 graduates.

= npq

= (370 x 0.50 x 0.50)

= 9.6177

b. The numbers of graduates among 370 who stay at their first job less than two years should usually fall between 175.4 and 194.6.

– 2 = 185- 9.6 = 175.4

+ 2 = 185+ 9.6 = 194.6

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