The diameter of small Nerf balls manufactured at a factory in China is expected to be approximately normally distributed with a mean of 5.2 inches and a standard deviation of .08 inches.Suppose a random sample of 20 balls is selected.Find the interval that contains 95.44% of the sample means.
A)[5.04 5.36]
B)[5.18 5.22]
C)[5.16 5.24]
D)[5.07 5.33]

Question

Quizplus · Accepted Answer

We need to use the formula for the confidence interval of the sample mean:

CI = X̄ ± z* (σ/√n)

Where X̄ is the sample mean, σ is the standard deviation, n is the sample size, and z* is the z-score corresponding to the desired confidence level.

In this case, we want a confidence level of 95.44%, which corresponds to a z-score of 1.781.

Substituting the given values into the formula, we get:

CI = 5.2 ± 1.781 * (0.08/√20) = [5.16, 5.24]

Therefore, the best choice is (C), [5.16, 5.24], which contains the interval with 95.44% of the sample means.

The Diameter of Small Nerf Balls Manufactured at a Factory