SOLUTION: a. The average age of employees is 24 yrs old with a standard deviation of 2.5yrs. If a random sample of 40 employees are selected, what would be the distribution of average ages

Question 1046130: a. The average age of employees is 24 yrs old with a standard deviation of 2.5yrs. If a random sample of 40 employees are selected, what would be the distribution of average ages from samples of this size look like? Why?
b. What would the be average for all sample means from samples of this size?
c. What would the standard error be for all sample means from samples of this size?
d. What is the probability if you randomly selected 40 employees and averaged their ages together that the sample mean would be between 23 and 25yrs?

Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
The mean of the sample means for all sample of size 40 will be 24 years old. The mean doesn't change.
The standard deviation does change, and it is sigma/sqrt (40), the sample size
That here is 2.5/sqrt (40)=0.395
The z value would be (xbar-mean)/0.395=-1/0.395 or 1/0.395
The z value is between + and - 2.523.
The probability it will be in that range is 0.9886 (rounding may change the final digit). That means that a single person may have a significant probability of being distant form the mean, but as you group people together, the average of all of them is much less likely to be.
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