Mean and standard deviation of m m bags labeled 169

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Mean and Standard Deviation of m & m Bags Labeled 1.69 oz. Do m&m bags labeled 1.69 oz. actually contain that weight? If not, what is a typical weight and how much variability is there from bag to bag? To answer those questions, we will collect data on ten bags of m&m’s. Your teacher or a volunteer will weigh each bag and report the weights. Your task is to use the tables below to calculate and interpret the mean and standard deviation for the weights of bags labeled 1.69 oz. As the data is collected, construct a dotplot and fill in the table below. 1.5 1.55 1.6 1.65 1.7 1.75 1.8 Weights of “1.69 oz” Bags of m&m’s Bag # x ( x ! x ) ( x ! x ) 2 1 2 3 4 5 6 7 8 9 10 n=10 x ! = _____ ( x ! x ) " ( x ! x ) " 2 x = _____ = ______ = ______ Standard Deviation s= ( x ! x ) 2 " n ! 1 s=________________. Everything I Ever Wanted to Know about AP Statistics I Learned From a Bag of m&m’s 8
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Standard Normal Calculations This activity can be used to illustrate practical uses of standard normal calculations and their interpretations. It is meant to reinforce the concept of normal distributions and individual observations as well as introduce students to the basic idea of inference. While students have not studied sampling distributions or inferential procedures, they should be able to use what they know about variability and normal distributions to make some basic inferential conclusions. Materials Needed: • 2 1.69 bags of milk chocolate m&m’s • At least 1 1.69 bag of peanut butter m&m’s Activity: Students should be familiar with the concept of normal distributions and should have a basic understanding of sampling variability. Discuss the fact that the proportion of yellow m&m’s in an individual bag will vary from bag to bag. Note that the proportion of yellow m&m’s in individual bags varies according to approximately N(0.14, 0.05). Sketch the distribution, noting where each standard deviation falls. Discuss the Empirical (68-95-99.7) Rule as it relates to the proportion of yellow m&m’s in a bag. Ask for student impressions of ‘extreme’ proportions. That is, at what point would they suspect the claim that 14% of m&m’s are yellow? Why would they suspect it? Estimate the percent of bags that have less than 10% yellow m&m’s, greater than 20% yellow, etc. Open milk chocolate m&m’s and note proportion of yellow candies. {Note: if this proportion is exactly 14%, you may wish to use another bag} Locate and plot this proportion on the normal curve. Calculate and interpret the standardized z-score and corresponding proportions above and below this value. If you have 2 bags, repeat the calculations and find the proportion of bags that would fall between the two observations. After exhausting all possible calculations with the milk chocolate m&m’s, open and find the proportion of yellow peanut butter m&m’s. {Note: 20% of peanut butter m&m’s are yellow, as compared to 14% of milk chocolate m&m’s--do not tell students this}. Locate this proportion on the N(0.14, 0.05) distribution and discuss whether or not they think yellow peanut butter m&m’s are produced in the same proportion as yellow milk chocolate m&m’s.
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