A previous analysis of paper boxes showed that the the standard deviation of their lengths is 15 millimeters. A packer wishes to find the 90% confidence interval for the average length of a box. How many boxes does he need to measure to be accurate within 3 millimeters?
A) 25
B) 97
C) 69
D) 41

Question

Quizplus · Accepted Answer

The formula for the sample size needed for a confidence interval is:
n = (z * σ / E)^2
Where n is the sample size, z is the z-score for the desired confidence interval (1.645 for 90% confidence), σ is the population standard deviation (given as 15 millimeters), and E is the margin of error desired (3 millimeters).

Plugging these values into the formula, we get:
n = (1.645 * 15 / 3)^2
n = 68.6

Since we cannot have a fraction of a box, we round up to the nearest whole number:
n = 69

Therefore, the packer needs to measure 69 boxes to be accurate within 3 millimeters with 90% confidence. The answer is C) 69.

A Previous Analysis of Paper Boxes Showed That the The Standard