Question

Thompson and Thompson is a steel bolts manufacturing company. Their current steel bolts have a mean diameter of 132 millimeters, and a variance of 64. If a random sample of 39 steel bolts is selected, what is the probability that the sample mean would be greater than 128.2 millimeters?

Answer 1

0.9985

Explanation:

The population standard deviation is:

s² = 64

s = 8

The sample standard deviation is:

σ = s/√n

σ = 8/√39

σ = 1.28

The z-score is:

z = (x − μ) / σ

z = (128.2 − 132) / 1.28

z = -2.97

The probability is:

P(Z > -2.97) = 1 − P(Z < -2.97)

P(Z > -2.97) = 1 − 0.0015

P(Z > -2.97) = 0.9985