Thompson and thompson is a steel bolts manufacturing company. their current steel bolts have a mean diameter of 134 millimeters, and a variance of 36. if a random sample of 44 steel bolts is selected, what is the probability that the sample mean would be greater than 135.4 millimeters? round your answer to four decimal places.

We are required to evaluate the following probability that the mean would be greater than 135.4 mm.
the z-score is given by:
z=(x-μ)/σ
where:
μ- mean
σ-standard deviation
thus
z=(135.4-134)/36
z=0.03889

hence:
P(X≥135.4)=1-P(Z=0.03889)=1-0.4840=0.516~51.6%

Answer: 0.516~51.6%