Thompson and Thompson is a steel bolts manufacturing company. Their current stee

Question

Thompson and Thompson is a steel bolts manufacturing company. Their current steel bolts have a mean diameter of 143 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 greater than 3.3 millimeters? Round your answer to four decimal places. Thompson and Thompson is a steel bolts manufacturing company. Their current steel bolts have a mean diameter of 143 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 greater than 3.3 millimeters? Round your answer to four decimal places. Thompson and Thompson is a steel bolts manufacturing company. Their current steel bolts have a mean diameter of 143 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 greater than 3.3 millimeters? Round your answer to four decimal places.

Explanation / Answer

mean diameter = 143

variance = 64

standard deviation = variance = 64 = 8

sample size = 32

standard deviation of sample mean = standard deviation/n = 8/32 = 1.4142

probability that the sample mean would differ from the population mean by greater than 3.3 millimeters = probability that the sample mean will be less than mean-3.3 or greater than mean+3.3

z value mean-3.3 = (mean-3.3-mean)/1.4142 = -3.3/1.4142 = -2.3335, corresponding p value using z table is 0.00981

P(X<mean-3.3) = 0.00981

By symmentry of nomal curve P(X<mean-3.3) = P(X>mean+3.3)

so P(X<mean-3.3) + P(X>mean+3.3) = 2*0.00981 = 0.0196

probability that the sample mean would differ from the population mean by greater than 3.3 millimeters is 0.0196

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