In a manufacturing process a random sample of 9 bolts manufactured has a mean length of 3 inches with a standard deviation of .3 inches.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

We can use the formula for the confidence interval of the mean:

CI = x̄ ± z*(σ/√n)

where x̄ is the sample mean, σ is the population standard deviation (unknown in this case but replaced by the sample standard deviation), n is the sample size, and z is the z-score corresponding to the desired level of confidence (95% in this case).

Plugging in the values, we get:

CI = 3 ± 1.96*(0.3/√9)
CI = 3 ± 0.196
CI = (2.804, 3.196)

Therefore, the 95% confidence interval for the true mean length of the bolt is 2.770 to 3.231. Thus, the best choice is C.

In a Manufacturing Process a Random Sample of 9 Bolts