Question

Thompson and Thompson is a steel bolts manufacturing company. Their current steel bolts have a mean diameter of 137 millimeters, and a standard deviation of 8 millimeters.If a random sample of 31 steel bolts is selected, what is the probability that the sample mean would be greater than 133.5 millimeters? Round your answer to four decimal places.

Answer 1

Answer:

The probability that the sample mean would be greater than 133.5 is 0.9926

Step-by-step explanation:

Given:

Mean = 137

Standard deviation = 8

Sample = 31

To find the probability that the sample mean would be greater than 133.5, we have:

`\begin{gathered} z=(X-\mu)/((\sigma)/(√(n))) \\ \\ =(133.5-137)/((8)/(√(31)))=-2.4359 \\ \\ P(X>133.5)=1-P(z<-2.4359) \\ =1-0.0074274 \\ \approx0.9926 \end{gathered}`