Question

Thompson and Thompson is a steel bolts manufacturing company. Their current steel bolts have a mean diameter of 135 millimeters, and a standard deviation of 5 millimeters.

If a random sample of 42 steel bolts is selected, what is the probability that the sample mean would differ from the population mean by more than 0.8 millimeters? Round your answer to four decimal places.

Answer 1

Solution :

Given that,

mean = = 135

standard deviation = = 5

= / n = 5 / 42 = 0.7715

= 1 - P[(-0.8) /0.7715 < ( - ) / < (0.8) / 0.7715)]

= 1 - P(-1.04 < Z < 1.04)

= 1 - P(Z < 1.04) - P(Z < -1.04)

= 1 - P(0.8508 - 0.1492)

= 1 - 0.7016

= 0.2984

Probability = 0.2984