In a manufacturing process a random sample of 9 bolts manufactured has a mean length of 3cm with a standard deviation of .3cm.Assuming bolt length is normally distributed,what is the 95% confidence interval for the true mean length of the bolt?
A)2.804 to 3.196
B)2.308 to 3.692
C)2.770 to 3.231
D)2.412 to 3.588
E)2.814 to 3.186

Question

Quizplus · Accepted Answer

The 95% confidence interval for the true mean length of the bolt can be calculated using the formula:
CI = X̄ ± 1.96 * (σ / √n)
where X̄ is the sample mean, σ is the population standard deviation (or sample standard deviation if the population standard deviation is unknown), n is the sample size, and 1.96 is the z-score for a 95% confidence level.

Substituting the given values, we get:
CI = 3 ± 1.96 * (0.3 / √9)
CI = 3 ± 0.196
CI = (2.804, 3.196)

Therefore, the best choice is C.

In a Manufacturing Process a Random Sample of 9 Bolts