In a manufacturing process,a random sample of 36 bolts has a mean length of 3 inches with a standard deviation of .3 inches.What is the 99 percent confidence interval for the true mean length of the bolt?
A)2.902 to 3.098
B)2.884 to 3.117
C)2.864 to 3.136
D)2.228 to 3.772
E)2.802 to 3.198

Question

Quizplus · Accepted Answer

We can use the formula for a confidence interval:

Confidence interval = sample mean ± (z-score)*(standard error)

Where the standard error is equal to the standard deviation divided by the square root of the sample size:

standard error = 0.3 / sqrt(36) = 0.05

The z-score for a 99% confidence interval is 2.576 (from a standard normal distribution table).

Plugging in the values, we get:

Confidence interval = 3 ± (2.576)*(0.05) = (2.864, 3.136)

Therefore, the answer is C, 2.864 to 3.136.

In a Manufacturing Process,a Random Sample of 36 Bolts Has