A local company makes snack-size bags of potato chips. Each day, the company produces batches of 400 snack-size bags using a process designed to fill each bag with an average of 2 ounces of potato chips. However, due to imperfect technology, the actual amount placed in a given bag varies. Assume the amount placed in each of the 400 bags is normally distributed and has a standard deviation of 0.1 ounce. What is the probability that a sample of 40 bags has an average weight of at least 2.02 ounces?
A) 0.0150
B) 0.0915
C) 0.1038
D) 0.4207

Question

Quizplus · Accepted Answer

Given that the distribution of weights in the bags is normal, we can use the Central Limit Theorem to find the probability concerning the sample mean. The standard deviation of the sample mean ($\sigma_{\bar{x}}$) is given by $\sigma/\sqrt{n}$, where $\sigma = 0.1$ ounces is the population standard deviation, and $n = 40$ is the sample size. Thus, $\sigma_{\bar{x}} = 0.1/\sqrt{40}$. To find the probability that the sample mean is at least 2.02 ounces, we calculate the Z-score for 2.02 ounces and use the standard normal distribution. The calculation leads to a probability that matches the option provided.

A Local Company Makes Snack-Size Bags of Potato Chips