Elementary Statistics with Probability

Question

Mars, Inc., claims that an average 12.5% of its M&M plain candies are green with a standard deviation of 3.31% at its New Jersey factory. Meanwhile, an average of 19.8% of them are green with a standard deviation of 3.99% at its Tennessee factory. When you select a random sample of 100 M&Ms, you find that there are 9 green candies in it. Is this result unusual? Which factory’s M&M do you think you were eating? Explain.

Answer 1

In the New Jersey factory, we can assume that out of 100 candies, 12.5 of them will be green. Likewise with the Tennessee factory, 19.8 of them will be green. Standard deviation, by loose definition is "distance away from the mean". In the case of this problem, the standard deviations for each of the factories (New Jersey and Tennessee respectively) is 3.31 and 3.99, meaning we can either add or subtract that number from the mean to get one standard deviation.

New Jersey Factory: 12.5%-3.31%= 9.19%

Tennessee Factory: 19.8%-3.99%= 15.81%

As you can see, the New Jersey factory will yield 9.19% green candies at one standard deviation away from the mean giving us our answer. In our sample of 100 candies, approximately 9 of them will be green. These results are usual. Remember, results are only unusual at > 2 standard deviations away from the mean. If you need any further help, feel free to message me. I would love to work with you through any other problems that you may have. I hope this helps.