In a manufacturing process,we are interested in measuring the average length of a certain type of bolt.Based on a preliminary sample of 9 bolts,the sample standard deviation is 0.3cm.If the lengths are normally distributed,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)864.36
B)80
C)1470
D)3989
E)1197

Question

Quizplus · Accepted Answer

We can use the formula for the margin of error:

Margin of error = z* (sigma/sqrt(n))

Where z* is the z-score corresponding to the confidence level of 95%, which is 1.96. Sigma is the population standard deviation, which is unknown, but we can use the sample standard deviation as an estimate because the sample size is large enough.

Solving for n, we get:

n = ((z* * sigma) / Margin of error)^2

Substituting the given values, we get:

n = ((1.96 * 0.3) / 0.02)^2

n ≈ 1197

Therefore, we need to sample 1197 bolts to be 95% confident that the sample mean bolt length is within 0.02cm of the true mean bolt length.

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