The weight of corn chips dispensed into a 14-ounce bag by the dispensing machine has been identified as possessing a normal distribution with a mean of 14.5 ounces and a standard deviation of 0.2 ounce. Suppose 100 bags of chips are randomly selected. Find the probability that the mean weight of these 100 bags exceeds 14.6 ounces.
A) .3085
B) .6915
C) .1915
D) approximately 0

Question

Quizplus · Accepted Answer

The standard error of the mean is 0.02 (0.2/√100). The z-score for 14.6 is (14.6-14.5)/0.02 = 5. A z-score of 5 corresponds to a very small probability, so the probability that the mean weight exceeds 14.6 ounces is approximately 0.

The Weight of Corn Chips Dispensed into a 14-Ounce Bag