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?
1 answer:
Answer:
0.9985
Step-by-step 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
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