Stats M and M .pdf

# Everything i ever wanted to know about ap statistics

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Everything I Ever Wanted to Know about AP Statistics I Learned From a Bag of m&m’s 9

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Are These m & m s Normal or Just Plain ? Standard Normal Calculations We have observed variability in color distributions from bag to bag of “plain” milk chocolate m&m’s. According to the m&m website, 14% of milk chocolate m&m’s are yellow. Does that mean we are guaranteed 14% of the candies in each bag will be yellow? Should you be concerned if only 10% are yellow? What if all of them are? At what point would you suspect the advertised proportion? We will discuss each of these questions as we explore standard normal calculations with some sample bags of m&m’s. Background Information: We know the proportion of yellow m&m’s varies from bag to bag. Suppose these proportions follow an approximately normal distribution N(0.14, 0.05). Sketch this distribution below and note 1, 2, and 3 standard deviations above and below the mean. Interpret the Empirical (68-95-99.7) Rule in the context of this situation. Sample Information: Our bag of m&m’s contained _____ candies. There were _______ yellow m&m’s. The sample proportion of yellow candies for our bag is _____/______ = _______. Standard Normal Calculation: Recall, a “z-score” is a value that tells us how many standard deviations above or below the mean a particular observation falls. To find this value, we must subtract the mean from our observation and divide the result by the standard deviation. That is, z = x ! x s = ! = We can use this z-score to determine what percent of bags of m&m’s (of the same size) would have a yellow proportion less than our observed proportion. Sketch two normal distributions for yellow proportions below and note our observed proportion on each curve. Using your z- table, determine the proportion of bags of the same size that would have fewer yellow candies. Shade this area on the first curve. On the second curve, shade and calculate the proportion of bags of the same size that would have more yellow candies. Everything I Ever Wanted to Know about AP Statistics I Learned From a Bag of m&m’s 10
Suppose we had a second bag of m&m’s. We would expect about 14% of the candies in the second bag would be yellow. However, like the first bag, there is a chance that proportion will not equal 0.14 (or the proportion in the first bag, for that matter). Use the proportions from the first bag and from a new bag to determine what percent of bags of m&m’s of the same size will have a yellow proportion between those two values. Bag 1 Bag 2 Yellow Proportion z-score % Bags Below Observed Sketch the two observed proportions on the normal distribution N(0.14, 0.05) and note the percent of observations we would expect to see between the two observed proportions. What About Peanut Butter m&m’s? Do peanut butter m&m’s follow the same color distribution as milk chocolate m&m’s? If so, we would expect about 14% of the candies in a peanut butter m&m bag would be yellow.

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• Fall '17

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