Answer
Average Salary For a Federal Employee In 2012 Was 74804. Assume The Population Standard Deviation Is
According to Fedsmith.com, the average salary for a federal employee in 2012 was $74804. Assume the population standard deviation is $ 15,300.
A random sample of 34 federal employees is selected. (i) What is the probability that the sample mean will be less than $70,000? (ii) What is the probability that the sample mean will be more than $74,000? (iii) What is the probability that the sample mean will be between $76,000 and $ 81,000?
Avg. salary of µ=$74,804,
Population standard deviation sigma= 15,300
deviation 
and the sample size of 
federal employees selected.
For the normal model, the formula for z-score of the sample mean is,
By the Central Limit Theorem (CLT), the mean of the sampling distribution of 
is the population mean 
. That is, 
.
.
Hence, the required probability is,
Thus, the probability that the sample mean will be less than $70,000 is 
.
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