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.What percentage of sample means will be less than 5.14 inches?
A)0.048%
B)22.66%
C)4.8%
D).00048%

Question

Quizplus · Accepted Answer

The z-score for a sample mean of 5.14 inches is (5.14 - 5.2) / (.08 / sqrt(20)) = -1.75. The percentage of sample means that will be less than 5.14 inches is the area under the normal distribution curve to the left of z = -1.75, which is approximately 0.048%.

The Diameter of Small Nerf Balls Manufactured at a Factory