Thompson and Thompson is a steel bolts manufacturing company. Their current steel bolts have a mean diameter of 135 millimeters, and a variance of 64. If a random sample of 32 steel bolts is selected, what is the probability that the sample mean would differ from the population mean by more than 3.6 millimeters? Round your answer to four decimal places.

0.3264

Step-by-step explanation:

The formula for calculating a z-score is is z = (x-μ)/σ, where

x is the raw score,

μ is the population mean,

σ is the population standard deviation.

(x-μ) = 3.6 mm

σ = √variance = √64 = 8mm

z = 3.6/8

z = 0.45

Using the Probability table

P(x<Z) = 0.67364

P(x>Z) = 1 - P(x<Z)

1 - 0.67364

= 0.32636

Approximately = 0.3264

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step-by-step explanation: