Question

The mean amount μ for all 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 $334. You take a random sample of 106 invoices. Apply the Central Limit Theorem and the 68-95-99.7 Rule to complete the following sentence: “The probability is about 0.95 that the sample mean is within _________ of the population mean μ.”

Enter your answer to 2 decimal places of accuracy.

Answer 1

Solution :

Given that

standard deviation = = 334

n = 106

= / n = 334 / 106 = 32.44

P( - 2 < <   + 2 ) = 95%

=   ± 2 = 95%

=    ± 2 * 32.44 = 95%

=   ± 64.88 = 95%

“The probability is about 0.95 that the sample mean is within 64.88 of the population mean μ.”