The weight of potato chip bags filled by a machine at a packaging plant is normally distributed, with a mean of 15.0 ounces and a standard deviation of 0.2 ounces. What is the probability that a randomly chosen bag will weigh less than 14.6 ounces?
A) 50%
B) 5%
C) 2.5%
D) 2%

Question

Quizplus · Accepted Answer

To find the probability that a bag weighs less than 14.6 ounces, we calculate the z-score for 14.6 ounces using the formula z = (X - μ) / σ, where X is the value (14.6 ounces), μ is the mean (15.0 ounces), and σ is the standard deviation (0.2 ounces). This gives us z = (14.6 - 15.0) / 0.2 = -2. The z-score of -2 corresponds to a probability of about 2.5% in the standard normal distribution table.

The Weight of Potato Chip Bags Filled by a Machine