Question

Thompson and Thompson is a steel bolts manufacturing company. Their current steel bolts have a mean diameter of 131 millimeters, and a standard deviation of 8 millimeters. If a random sample of 50 steel bolts is selected, what is the probability that the sample mean would differ from the population mean by more than 3 millimeters? Round your answer to four decimal places.

Answer 1

for normal distribution z score =(X-μ)/σx
here mean=       μ=	131
std deviation   =σ=	8.000
sample size       =n=	50
std error=σx̅=σ/√n=	1.13137

probability that the sample mean would differ from the population mean by more than 3 millimeters:

probability =1-P(128<X<134)=1-P((128-131)/1.131)<Z<(134-131)/1.131)=1-P(-2.65<Z<2.65)=1-(0.996-0.004)=0.0080