A machine that produces a major part for an airplane engine is monitored closely. In the past, 10% of the parts produced would be defective. With a .95 probability, the sample size that needs to be taken if the desired margin of error is .04 or less is
A)110
B)111
C)216
D)217

Question

Quizplus · Accepted Answer

To determine the sample size, we must first find the critical value associated with a 95% confidence level. Using a standard normal distribution table, this value is 1.96.

Next, we can use the formula:

n = (Z^2 * p * q) / E^2

where: 
- n = sample size 
- Z = the critical value 
- p = the population proportion of defective parts 
- q = (1 - p) 
- E = the desired margin of error

Plugging in the values given: 
n = (1.96^2 * 0.1 * 0.9) / 0.04^2 
n = 216.27

Rounding up to the nearest whole number, we get a sample size of 217.

Therefore, the best choice is D.

A Machine That Produces a Major Part for an Airplane