Thompson and Thompson is a steel bolts manufacturing company. Their current steel bolts have a mean diameter of 147 millimeters, and a variance of 36.
If a random sample of 43 steel bolts is selected, what is the probability that the sample mean would differ from the population mean by greater than 2.2 millimeters? Round your answer to four decimal places.
Solution :
Given that,
mean = = 147
standard deviation = = 6
_{} = / n = 6 / 43 = 0.9150
= 1 - P[(-2.2) /0.9150 < ( - _{}) / _{} < (2.2) / 0.9150)]
= 1 - P(-2.40 < Z < 2.40)
= 1 - P(Z < 2.40) - P(Z < -2.40)
= 1 - P(0.9918 - 0.0082)
= 1 - 0.9836
= 0.0164
Probability = 0.0164
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