In a sample of 80 nails of a particular type the average wei

In a sample of 80 nails of a particular type, the average weight was 1.54 g and the standard deviation was 0.1 g. Part 1 out of 5 a. Find a 95% confidence interval for the mean weight of this type of nail. Round to four decimal places. The confidence interval is

Solution

Given a=1-0.95=0.05, Z(0.025) = 1.96 (from standard deviation)

So the lower bound is

xbar - Z*s/vn = 1.54-1.96*0.1/sqrt(80) =1.5181

So the upper bound is

xbar + Z*s/vn = 1.54+1.96*0.1/sqrt(80) =1.5619