Final answer:
The question involves finding the probability for a normally distributed variable, specifically chocolate chip cookies in a bag, with a mean and standard deviation provided. Without a specific range, it's impossible to calculate an exact probability, but if one were given, we could use z-scores and a z-table to find the likelihood of the sample mean falling within that range.
Step-by-step explanation:
The question is asking for the probability that a 16-ounce bag of chocolate chip cookies follows a normal distribution with a given mean (µ) of 1252 chips and a standard deviation (σ) of 129 chips. To solve such a problem, one would typically need to specify a range of values to calculate the probability for that range under the normal distribution curve. Without a specific range or value to target, we cannot provide an exact probability. However, if you are interested in assuming that this situation aligns with a common type of problem where we need to calculate the likelihood of a sample mean falling within a certain range, you would use the standard normal distribution (z-scores) and a z-table or statistical software.
For example, in the context of quality control, a manufacturer might want to know the probability that a bag of cookies contains between 1200 and 1300 chips. They would calculate the z-scores for both 1200 and 1300, and then use the z-table to find the probabilities for these scores. The difference between these probabilities would provide the answer.
This process is directly related to the central limit theorem, which implies that as the sample size gets larger, the distribution of the sample mean will approach a normal distribution, even if the population distribution is not normal, as long as the population distribution has a finite variance.