Suppose a population is such that the population percent for "success" is 0.13. Consider drawing random samples of size 100 from this population, and counting the number of "successes" in the samples. Using technology, design and carry out a simulation that will produce a simulated sampling distribution in this situation. Based on your simulated sampling distribution, what sample outcomes would you consider to be rare events?

M&M'S® Milk Chocolate Candies have been a popular treat ever since they were first manufactured in 1940. The candies come in different colors. Red candies were discontinued in 1976 due to concerns about food coloring, but by popular demand the color red was brought back in 1987. Today, M&M'S® Milk Chocolate Candies are produced so that there are 13% reds. Suppose you are a quality control manager at the M&M® factory. Part of your job is to make sure the factory produces the correct percentage of reds, that is, 13% reds. If this correct percentage is not produced then the machines need to be shut down and reset, which is a very expensive process. Suppose you pull a random sample of 100 M&M'S® from the production line and you count 15 reds. Should you order the machines to be shut down and fixed? Explain and carry out the analysis and reasoning you would do to answer this question. (In fact, a quality control manager would probably pull several samples over time and use Statistical Process Control to help make her decision. In this problem, just assume that a single sample is drawn and use appropriate statistical reasoning to help make a decision.)

The given sampling distribution (provided) is based on counting the number of "successes" in random samples of size 100 drawn from a population in which the population percent for "success" is 0.13. Suppose you draw a random sample of 100 and count 15 "successes." Show where this sample outcome would appear in the sampling distribution. Would you consider this sample outcome to be a "rare event?" Explain.

M&M'S® Milk Chocolate Candies are produced so that there are 13% reds. Suppose you are a quality control manager at the M&M® factory. Part of your job is to make sure the factory produces the correct percentage of reds, that is, 13% reds. If this correct percentage is not produced then the machines need to be shut down and reset, which is a very expensive process. Suppose you draw a random sample of 100 M&M'S® and count 15 reds. You compare this sample outcome to the given sampling distribution for this situation (provided). Should you order the machines to be shut down and fixed? Explain.