Question

A machine used to fill beverage cans is supposed to put exactly 12 ounces of beverage in each can, but the actual amount varies randomly from can to can. The population standard deviation is 0.05 ounces. A simple random sample of filled cans will have their volumes measured, and a 95% confidence interval for the mean fill volume will be constructed. How many cans must be sampled for a margin of error to be equal to 0.01 ounces?

A. 385

B. 169

C. 625

D. 961

Answer 1

To determine the sample size needed for a margin of error of 0.01 ounces, use the formula n = (Z * σ) / E, where Z is the z-score, σ is the population standard deviation, and E is the margin of error. Plugging in the given values, the sample size required is 10 cans.

Step-by-step explanation:

To determine the sample size needed for a margin of error of 0.01 ounces, we need to use the formula:

n = (Z * σ) / E

Where:

n is the sample size

Z is the z-score corresponding to the desired confidence level

σ is the population standard deviation

E is the margin of error

In this case, the z-score for a 95% confidence level is approximately 1.96. The population standard deviation is given as 0.05 ounces, and the desired margin of error is 0.01 ounces.

Plugging in these values:

n = (1.96 * 0.05) / 0.01

n = 9.8

Since it is not possible to have a fraction of a can, we round up to the nearest whole number. Therefore, 10 cans must be sampled for a margin of error of 0.01 ounces.