In a manufacturing process,we are interested in measuring the average length of a certain type of bolt.Past data indicates that the lengths are normally distributed with standard deviation 0.25cm.How many bolts should be sampled in order to make us 95% confident that the sample mean bolt length is within 0.02cm 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 sample size calculation for a mean:

n = (zα/2 * σ / E)^2

where:
- n is the sample size
- zα/2 is the critical value for the desired level of confidence (95% in this case), which corresponds to 1.96
- σ is the population standard deviation, which is 0.25cm
- E is the margin of error, which is 0.02cm

Substituting these values, we get:
n = (1.96 * 0.25 / 0.02)^2 = 601.06

We should always round up to the nearest integer sample size, so the answer is 602.
Therefore, the best choice is D (601).

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