In a manufacturing process a random sample of 36 bolts manufactured has a mean length of 3 inches with a standard deviation of .3 inches.What is the 99% confidence interval for the true mean length of the bolt?
A)2.902 to 3.098
B)2.884 to 3.117
C)2.865 to 3.136
D)2.228 to 3.772
E)2.685 to 3.698

Question

Quizplus · Accepted Answer

We can use the formula: 
Confidence Interval = sample mean ± (critical value) x (standard error)
where the critical value can be found using a t-distribution table at 99% confidence level with degrees of freedom = n-1 = 35. From the table, we find the critical value to be 2.728.

The standard error can be calculated as standard deviation / sqrt(n) = 0.3 / sqrt(36) = 0.05.

Thus, the confidence interval is:
3 ± 2.728 x 0.05
= 3 ± 0.136
= (2.864, 3.136)

Therefore, the best choice is C, which matches the calculated confidence interval.

In a Manufacturing Process a Random Sample of 36 Bolts