Question

A previous analysis of paper boxes showed that the the standard deviation of their lengths is 11 millimeters. A packer wishes to find the 95% confidence interval for the average length of a box. How many boxes does he need to measure to be accurate within 4 millimeters?

Answer 1

To find the number of boxes the packer needs to measure in order to be accurate within 4 millimeters, the formula for the margin of error in a confidence interval is used.

Step-by-step explanation:

To find the number of boxes the packer needs to measure in order to be accurate within 4 millimeters, we can use the formula for the margin of error in a confidence interval:

Margin of error = Z * (standard deviation / sqrt(n))

Here, Z represents the z-score associated with the desired confidence level, standard deviation represents the known standard deviation of the lengths, and n represents the sample size.

In this case, we want to find the sample size (n) that results in a margin of error of 4 millimeters. Given that the desired confidence level is 95%, we can use a z-score of approximately 1.96.

Using the formula and solving for n:

4 = 1.96 * (11 / sqrt(n))

Squaring both sides and solving for n:

n = ((1.96 * 11) / 4)^2

n ≈ 75.9916

Rounded up to the nearest whole number, the packer needs to measure at least 76 boxes to be accurate within 4 millimeters.