A laboratory scale is known to have a standard deviation of

A laboratory scale is known to have a standard deviation of ? = 0.003 gram in repeated weighings. Scale readings in repeated weighings are Normally distributed, with mean equal to the true weight of the specimen. Five weighings of a specimen on the scale give an average of 3.414 grams. A 95% confidence interval for the true weight is which of the following?

3.414

Solution

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

So 95% confidence interval is

xbar +/- Z*s/vn

--> 3.414 +/- 1.96*0.003/sqrt(5)

--> 3.414 +/- 0.00263