Please solve with explanation The shaft diameters in a sampl

Please solve with explanation

The shaft diameters in a sample of 25 shafts are measured. The sample mean of diameter is 0.102cm, with a standard deviation of 0.005cm. What is the upper 95% confidence limit on the mean diameter of all shafts produced by this process, assuming that the distribution of shaft diameters is normal?

Solution

The degree of freedom =n-1=25-1=24

Given a=1-0.95=0.05, t(0.025, df=24) =2.06 (from student t table)

So the upper limit is

xbar- t*s/vn= 0.102-2.06*0.005/sqrt(25) =0.09994