Question

A machine on an assembly line fills cans with quantities of food that are normally distributed with a standard deviation of 0.057 pounds. The mean quantity filled is estimated using a sample of 100 cans. What is the difference between the upper and lower limits of the 95% confidence interval for the mean? A. 0.0057 lb. B. 0.011 lb. C. 0.022 lb. D. 0.11 lb. E. 0.22 lb.

Answer 1

The difference between the upper and lower limits of the confidence interval would be 0.22344, or answer choice E.

Explanation:

To find the width of the confidence interval, one only needs to know the standard error and the confidence level, not the point estimate.

In the problem we are given that the standard deviation is .057.

They say that the confidence level is 95%, which is equal to 1.96 (that value can be found using the inverse normal function on a calculator or from a z-table).

.057×1.96=.11172. This is the value that would be added on to the point estimate to find the upper bound and subtracted to find the lower bound. Using this logic, there would be two of this number between the upper and lower limits of the confidence interval, so .11172×2=.22344.