Question

The popular candy Skittles comes in five colors. According to the Skittles website, the five colors are evenly distributed in the population of Skittle candies, so each color makes up 20% of the population. Suppose that we purchase a small bag of Skittles. Assume that this size bag always has 20 candies. In this particular bag, 6 are green: 6 out of 20 is 30%. Is this a surprising result? Use the applet to conduct a simulation. Which option gives the right answer and the best explanation? Group of answer choices Yes, this result is surprising. Random samples with this much error are unusual. Yes, this result is surprising. We expect 20% of candies to be green. No, this result is not surprising. It is a little bit more than one standard deviation above 20%. No, this result is not surprising. We expect random samples to vary.

Answer 1

No, this result is not surprising. It is a little bit more than one standard deviation above 20%

Explanation:

Proportion of each color in the population (p) = 0.20

Sample size (n) = 20 Skittles

The standard deviation of a sampling distribution is determined by:

`\sigma = \sqrt{(p*(1-p))/(n)}\\\sigma = \sqrt{(0.20*(1-0.20))/(20)}\\ \sigma =0.089`

The difference between the observed proportion of 0.30, and the mean proportion of 0.20 is 0.10, which is just a little bit more than one standard deviation of 0.089. Therefore, this result is not surprising since it is a little bit more than one standard deviation above 20%.