In a manufacturing process,we are interested in measuring the average length of a certain type of bolt.Past data indicates that the standard deviation is .25 inches.How many bolts should be sampled in order to make us 95% confident that the sample mean bolt length is within .02 inches of the true mean bolt length?
A)25
B)49
C)423
D)601
E)1225

Question

Quizplus · Accepted Answer

We need to use the formula for the margin of error:
Margin of error = z * (standard deviation / sqrt(n))
Here, we want the margin of error to be no more than .02 inches, and we want to be 95% confident, so we need to find the z-score for the 97.5th percentile, which is 1.96. Substituting in the given data, we can solve for n:
.02 = 1.96 * (.25 / sqrt(n))
Solving for n, we get n = 601. Answer choice (D) is the closest option to this value, so it is the best choice.

In a Manufacturing Process,we Are Interested in Measuring the Average