4 20 points Softdrink cans are lled by an automated lling ma

4. 20 points Soft-drink cans are lled by an automated lling machine. The mean ll volume is 12.1 uid ounces and the standard deviation is 0.5 uid ounces. Assume that the ll volumes of the cans are independent, normal random variables. What is the probability that the average ll volume of 40 cans is below 12 uid ounces

Solution

mean = 12

std dev = 0.5

For x = 12, the z-value z = (12 - 12.1) / 0.5 = -0.2

Hence P(x < 12) = P(z < -0.2) = [area to the left of 2.5] = 0.4207