The diameter of small Nerf balls manufactured at a factory i

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 are selected. What percentage of sample means will be less than 5.15 inches? (Ch8)

Solution

Let X - The diameter of small Nerf balls manufactured at a factory in China

X is normal (5.2, 0.08)

n=20

Sample std error = 0.08/rt 20 = 0.0179

Z for x = 5.15 is -0.05/0.0179 = 0.0009

Hence P(X<5.15) = 0.5