Question

The distribution of weights of 9-ounce bags of a particular brand of potato chips is approximately normal with a mean of 9.12 ounces and a standard deviation of 0.05 ounce. What proportion of bags weigh between 8.97 and 9.17 ounces?

Answer 1

To find the proportion of bags that weigh between 8.97 and 9.17 ounces, calculate the z-scores for each weight and find the area between these z-scores under the standard normal curve.

Step-by-step explanation:

To find the proportion of bags that weigh between 8.97 and 9.17 ounces, we need to calculate the z-scores for each of these weights and then find the area between these two z-scores under the standard normal curve.

First, we calculate the z-score for 8.97 ounces:

z = (8.97 - 9.12) / 0.05 = -3.00

Next, we calculate the z-score for 9.17 ounces:

z = (9.17 - 9.12) / 0.05 = 1.00

Using a standard normal distribution table or a calculator, we can find the proportion of bags that have weights less than 8.97 ounces (which is the same as finding the area to the left of -3.00) and the proportion of bags that have weights less than 9.17 ounces (which is the same as finding the area to the left of 1.00). Finally, we subtract the proportion of bags that weigh less than 8.97 ounces from the proportion that weigh less than 9.17 ounces to find the proportion that weigh between these two weights.