Question

Thompson and Thompson is a steel bolts manufacturing company. Their current steel bolts have a mean diameter of 149149 millimeters, and a standard deviation of 88 millimeters.

If a random sample of 5050 steel bolts is selected, what is the probability that the sample mean would differ from the population mean by more than 3.33.3 millimeters? Round your answer to four decimal places.

Answer 1

Solution :

Given that,

mean = = 149

standard deviation = = 8

n = 50

= 149

= / n = 8 / 50

= 1 - P[-3.3 / 8 / 50 < ( - ) / < 3.3 / 8 / 50 )]

= 1 - P(-2.92 < Z < 2.92)

= 1 - P(Z < 2.92) - P(Z < -2.92)

= 0.0035