Measurements of the diameters of a random sample of 200 ball

Measurements of the diameters of a random sample of 200 ball bearings made by a certain machine during one week showed a mean of 0.824 inches and a standard deviation of 0.042 inches. Find the bounds of the 90% confidence interval for the mean diameter of all the ball bearings.

0.816 ?

Solution

Given a=1-0.9=0.1, Z(0.05) = 1.645 (from standard normal table)

So the lower bound is

xbar - Z*s/vn =0.824 -1.645*0.042/sqrt(200) =0.8191146

So the upper bound is

xbar + Z*s/vn =0.824 +1.645*0.042/sqrt(200) =0.8288854

Answer: 0.8191 ?