Final answer:
Approximately 68.26% of the 16-ounce bags of chocolate chip cookies will contain between 16.0 and 16.2 ounces, as calculated using z-scores and the standard normal distribution.
Step-by-step explanation:
To determine what percentage of 16-ounce bags of chocolate chip cookies contain between 16.0 and 16.2 ounces, we can use the properties of the normal distribution.
Given that the actual mean weight of the bags is 16.1 ounces and the standard deviation is 0.1 ounce, we can calculate the z-scores for 16.0 ounces and 16.2 ounces respectively.
The z-score for a value x is given by the formula z = (x - μ) / σ, where μ is the mean and σ is the standard deviation.
For x = 16.0, the z-score is z = (16.0 - 16.1) / 0.1 = -1.
For x = 16.2, the z-score is z = (16.2 - 16.1) / 0.1 = 1.
Referring to standard normal distribution tables or using a calculator, we find the area under the normal curve between z = -1 and z = 1.
This area corresponds to the percentage of bags weighing between 16.0 and 16.2 ounces. The area between z = -1 and z = 1 is approximately 68.26%.
Therefore, approximately 68.26% of the bags will contain between 16.0 and 16.2 ounces of cookies.