Based on historical data,the diameter of a ball bearing is normally distributed with a mean of 0.527 cm and a standard deviation of 0.008 cm.Suppose that a sample of 18 ball bearings are randomly selected from a very large lot.Determine the probability that the average diameter of a sampled ball bearing is greater than 0.530 cm.
A)0.2324
B)0.4938
C)0.5062
D)0.0559

Question

Quizplus · Accepted Answer

We can use the central limit theorem to approximate the sampling distribution of the sample mean.

The mean and standard deviation of the sampling distribution of the sample mean are:

μx = μ = 0.527 cm
σx = σ/√n = 0.008 cm/√18 ≈ 0.00189 cm

Therefore, we need to find the probability that a standardized sample mean is greater than:

z = (0.530 - 0.527) / 0.00189 ≈ 1.5873

Using a standard normal table or calculator, we find:

P(Z > 1.5873) ≈ 0.0559

Therefore, the probability that the average diameter of a sampled ball bearing is greater than 0.530 cm is approximately 0.0559. The correct answer is (D).

Based on Historical Data,the Diameter of a Ball Bearing Is