In a manufacturing process,a machine produces bolts that have an average length of 3 inches with a variance of .03.If we randomly select three bolts from this process,What is the probability the mean length of the bolt is at least 3.16 inches?
A)97.72%
B)5.48%
C)94.52%
D)44.52%
E)2.28%

Question

Quizplus · Accepted Answer

We know that the distribution of the bolt lengths follows a normal distribution with mean = 3 and variance = 0.03. The standard deviation is therefore sqrt(0.03) = 0.1732.
To calculate the probability that the mean length of three bolts is at least 3.16 inches, we need to convert this to a standardized z-score.
z = (3.16 - 3) / (0.1732 / sqrt(3)) = 2.48
Using a standard normal distribution table or calculator, we find that the probability of obtaining a z-score of 2.48 or greater is approximately 0.0548 or 5.48%.
Therefore, the best choice is B.

In a Manufacturing Process,a Machine Produces Bolts That Have an Average