Question

Suppose a batch of metal shafts produced in a manufacturing company have a variance of 9 and a mean diameter of 207 inches.

If 72 shafts are sampled at random from the batch, what is the probability that the mean diameter of the sample shafts would be less than 206.7inches? Round your answer to four decimal places.

Answer 1

Solution:

Given: a batch of metal shafts produced in a manufacturing company have a variance of 9 and a mean diameter of 207 inches.

that is: Mean = and Standard Deviation =

Sample size = n = 72 > 30 , thus we can assume large sample size and hence applying Central limit theorem, the sampling distribution of sample means is approximate normal distribution.

We have to find: the probability that the mean diameter of the sample shafts would be less than 206.7inches

that is:

Find z score:

thus we get:

Look in the z table for z = -0.8 and 0.05 and find corresponding area.

P( Z < -0.85) = 0.1977

Thus

Thus the probability that the mean diameter of the sample shafts would be less than 206.7inches is 0.1977