This is a population standard deviation. The differences between sample standard deviation and population standard deviation are population standard deviation is calculated for a population, while sample standard deviation is calculated for a sample. Population standard deviation is designed with , sample standard deviation is designed with s. Population standard deviation is calculated with the formula =n(xix)2, sample population standard deviation is calculated with the formula s=n1(xix)2. Parameters of the normal distribution's=14 days =3 days (Population mean). (Population standard deviation).

Looking at probability that an employee takes less than 10 days. This is the calculation.

X-value

X0 =10 Days

Z - score

Z =-4^3/3=-1.33

Z table -1.33 is found by reading down column z to the row -1.3 then probability selection labeled 0.03 to be .0918

P(X<10 days)=9.18

More than 21 days

P(X>21 days ) = P(z>2.33)

Following the table to row 2.3 then probility labeled .003 to be .9901.

Probability.

P(X>21 days) =1-0.9901

P(x>21 days) = 0.0099

Probability is less than .05 this is unusual event

P(X>21 days) = .99%

The employees are more likely to take less than 10 days

• 1 hour ago

Hello Corey,

Great analysis! How would you used the results to determine the probability that an employee would take between 10 and 21 days vacation?