Question

The distribution of actual weights of 8 oz chocolate bars produced by a certain machine is normal with mean 7.7 ounces and standard deviation 0.15 ounces.

a. What is the probability that the average weight of a SRS of three of these chocolate bars in between 7.52 and 7.9 ounces? ____
b. For a SRS of three of these chocolate bars, what is the level L such that there is a 1% chance that the average weight is less than L? _____________

Answer 1

The questions relate to statistical methods and probability theory mainly focused on the normal distribution, with applications in calculating probabilities, sample means, and standard deviations for production quality control and hypothesis testing in different contexts.

Step-by-step explanation:

The questions presented involve the application of statistical methods and probability theory in different contexts such as quality control, sample distributions, and hypothesis testing. The main focus is on calculating probabilities, determining sample means, and establishing standard deviations for given distributions.

For example, in a scenario where chocolate bars are produced with a normal distribution of weights, and we have a mean weight of 7.7 ounces with a standard deviation of 0.15 ounces, we can use the properties of the normal distribution to answer questions about the probability that the average weight of a simple random sample (SRS) of chocolate bars falls within a certain range, or to find a specific weight threshold associated with a given probability.

To answer these types of questions, we often use the Z-score formula, which requires the mean and standard deviation of the distribution, as well as the mean and standard deviation of the sampling distribution of the sample mean, which is the standard deviation of the population divided by the square root of the sample size.