Question

Ask Your Teacher The mean amount μ for all of the invoices for your company last month is not known. Based on your past experience, you are willing to assume that the standard deviation of invoice amounts is about $250. If you take a random sample of 110 invoices, what is the value of the standard deviation for x?

Answer 1

The standard deviation for X bar is equal to the standard deviation ($250) divided by the square root of the sample size (110 invoices):

standard deviation for X bar = 250 / √110 = 250 / 10.49 = 23.82

The standard deviation for X bar gives us the sampling distribution of the sample mean. As the sample size increases, the X bar should approach the normal distribution.