The candy company claims that 10% of the M&Ms it produces are green. S

QUESTION

The candy company claims that 10% of the M&Ms it produces are green. Suppose that the candies are packaged at random in small bags containing about 50 M&Ms . A class of elementary school students learning about percents opens several bags, counts the various colors of the candies and calculates the proportions that are green.
a) if we plot a histogram showing the proportions of green candies in the varius bags, what shape would you expect it to have?
b) can that histogram be approximated by a Normal Model?explain
c) Where should the center of the histogram be?
d) what should the standard deviation of the proportion be?
Solution: (a) If we plot a histogram for the proportion of green candies in the bags, we would expect it to have spiked appearance due to the binomial distribution. (b) Number of Candies (n) = 50 Probability of green Candy (p) = 10% = 0.10 Expected Number of green M&M = Number of Candies (n)* Probability of green Candy (p) = 50*0.10 = 5 Since the expected number of green M&Ms is 5 which is less than 10 so the Normal model cannot be used to approximate the histogram. (c) The center of histogram should be around the expected¦

rtion of green M&Ms that means around 0.10. (d) Probability of green M&M (p) = 0.10 Probability of not green M&M (q) = 1 “ 0.10 = 0.90 Standard Deviation = (Probability of green M&M (p)* Probability of not green M&M (q)/ Number of Candies (n))^(1/2) So, Standard Deviation = (0.10*0.90/50) = 0.0424 Therefore, standard deviation is 0.0424.

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