Question

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.

Answer 1

Probability is 0.0174

Explanation:

Given data

mean = 140

variance = 25

no of sample n = 49

to find out

probability of the sample

solution

standard deviation is
`√(variance)`

standard deviation =
`√(25)`

standard deviation = 5

we mean by more than 1.7 millimeters so

mean (X1) = mean + 1.7 or mean - 1.7

so probability = X1 -mean/ ( standard deviation /
`√(n)` )

probability = 140 -1.7 -140 / ( 5 /
`√(49)` )

probability = - 1.7 / 35 = -0.048

probability = 140 + 1.6 -140 / ( 5 /
`√(49)` )

probability = 1.7 /35 = 0.048

so 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

= 0.0174

so required probability is 0.0174