A headline in a certain newspaper states that most stay at first job less than t

Question

A headline in a certain newspaper states that most stay at first job less than two years. That headline is based on an online poll of 370 college graduates among those polled 77% stayed at their first full-time job less than two years complete Parts a through d

a. assuming that 50% is the true percentage of graduates who stayed 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:
The standard deviation is:
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 job less than 2 years. use ascending order
c. find the actual number of surveyed graduates who stayed at their job less than 2 years use the range of values from Part B to determine whether the number is unusual does the results suggest that the headline is not justified round to the nearest whole number
d. is the actual number of surveyed graduates who stayed at their first job less than 2 years usual why

Explanation / Answer

a) here p=0.5 and n=370

mean=np=370*0.5=185

std deviation=(np(1-p))1/2 =9.6177

b) as usual values are 2 std deviation away from mean

therefore range of usual value =mean -/+ 2*std deviation =185 -/+2*9.6177 =165.76 ; 204.24

c)actual number of surveyed graduates who stayed at their job less than 2 years=370*0.77=284.9~285

as 285 is not in range of usual values; therefore the number is unusual

d)from above as actual number of surveyed graduates who stayed at their first job less than 2 years is beyond usual values range; therefore it is unusual

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