Question

The number of employees per department are normally distributed with a population standard deviation of 198 employees and an unknown population mean. If a random sample of 22 departments is taken and results in a sample mean of 1460 employees, find the error bound (EBM) of the confidence interval with a 80% confidence level.

Answer 1

EBM = +-54.126

Explanation:

In this question we have confidence interval to be 80%

The formula to solve this is in the attachment.

Bar X = 1460

Z-alpha/2 = 1.282

Sd = standard deviation = 198 employees

n = 22 departments

After we have inserted all values in to the formula we have:

1460 +-(1.282*198/√22)

= 1460+-(54.12604)

= (1405.87, 1514.126)

The error bounded mean EBM

= +-z-alpha/2 x (sd/√n)

= 1.282 x 198/√22

= 1.282 x 42.22

EBM = +-54.126