Question

Thompson and Thompson is a steel bolts manufacturing company. Their current steel bolts have a mean diameter of 142 millimeters, and a standard deviation of 6 millimeters. If a random sample of 35 steel bolts is selected, what is the probability that the sample mean would be greater than 139.7 millimeters? Round your answer to four decimal places.

Answer 1

Answer: 0.9884

Step-by-step explanation:

Given :  Population mean : $\mu=142$

and standard deviation : $\sigma=6$

sample size : n= 35

Let x be the random variable that represents the diameter of steel bolts.

Using formula $z=\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}$ ,

The z-value corresponds to x=139.7

$z=\dfrac{139.7-142}{\dfrac{6}{\sqrt{35}}}\approx-2.27$

The probability that the sample mean would be greater than 139.7 millimeters will be :-

$P(x>139.7)=P(z>-2.27)=1-P(z<-2.27)\\\\=1-(1-P(z<2.27))=P(z<2.27)\\\\=0.9883962\approx0.9884$

Hence, the required probability : = 0.9884