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 percent 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

To find the interval that contains 95.44% of the sample means, we need to use the formula:
interval = mean ± z* (standard error)
where mean = 5.2 inches (given), z* is the z-score corresponding to the desired confidence level and standard error = standard deviation / sqrt(sample size).
First, we need to find the z-score that corresponds to a 95.44% confidence level. Using a standard normal table or calculator, we find that the z-score is approximately 1.81 (rounding to two decimal places).
Next, we need to calculate the standard error:
standard error = 0.08 / sqrt(20) = 0.0179 (rounded to four decimal places).
Substituting the values into the formula, we get:
interval = 5.2 ± 1.81 * 0.0179
interval = [5.16, 5.24]
Therefore, the best choice is C, which contains the calculated interval.

The Diameter of Small Nerf Balls Manufactured at a Factory