Q:

Thompson and Thompson is a steel bolts manufacturing company. Their current steel bolts have a mean diameter of 141 millimeters, and a variance of 25.If a random sample of 49steel bolts is selected, what is the probability that the sample mean would differ from the population mean by more than 1.7 millimeters? Round your answer to four decimal places.

Accepted Solution

A:
Answer:Probability is 0.0174Step-by-step explanation:Given data mean = 140variance = 25no of sample n  = 49to find out probability of the samplesolutionstandard deviation is [tex]\sqrt{variance}[/tex]standard deviation = [tex]\sqrt{25}[/tex]standard deviation = 5we mean by more than 1.7 millimeters so mean (X1) = mean + 1.7 or mean - 1.7so probability = X1 -mean/ ( standard deviation / [tex]\sqrt{n}[/tex] ) probability = 140 -1.7 -140 / ( 5 / [tex]\sqrt{49}[/tex] ) probability = - 1.7 / 35 = -0.048 probability = 140 + 1.6 -140 / ( 5 / [tex]\sqrt{49}[/tex] ) probability = 1.7 /35 = 0.048so required  probability is  i.e= P(X1 < mean - 1.7 ∪ X1  > mean + 1.7 )= 1 - P(mean -1.7  < X1 < mean +1.7 ) = 1 - P(-0.048 < X1 < 0.048 )= 1 - 0.9826 = 0.0174so required  probability is 0.0174