Thompson and Thompson is a steel bolts manufacturing company. Their current steel bolts have a mean diameter of 145 millimeters, and a standard deviation of 7 millimeters.
If a random sample of 31 steel bolts is selected, what is the probability that the sample mean would be greater than 141.5 millimeters? Round your answer to four decimal places.
Solution :
Given that ,
mean = = 145
standard deviation = = 7
n = 31
_{} = 145
_{} = / n = 7 / 31
P( > 141.5) = 1 - P( < 141.5)
= 1 - P[( - _{} ) / _{} < (141.5 - 145) / 7 / 31 ]
= 1 - P(z < -2.78)
= 0.9973
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