Q.2.3 - The Practice of Statistics for AP

Question

Mars, Incorporated, says that the mix of colors in its M&M’S® Milk Chocolate Candies is $24\%$ blue, $20\%$ orange, $16\%$ green,$14\%$ yellow, $13\%$ red, and $13\%$ brown. Assume that the company’s claim is true. We want to examine the proportion of orange M&M’S in repeated random samples of $50$ candies. Which of the graphs that follow could be the approximate sampling distribution of the statistic? Explain your choice

Step-by-Step Solution

Answer

The Graph

 The second figure is appropriate for the sampling distribution of statistic. 

Step 1 Given Information

Given that mars, Incorporated, says that the mix of colors in its M&M’S® Milk Chocolate Candies is $24\%$ blue, $20\%$ orange, $16\%$ green, $14\%$ yellow, $13\%$red, and $13\%$ brown.

Assume that the company’s claim is true

Step 2 Explanation With Graph

The percentages of milk, blue, orange, green, yellow, red, and brown are$24\%,20\%,16\%,14\%,13\%\text{ and }13\%$ candies in M\&M's milk chocolate.

The number of candies is $50$

It is known that the proportion of orange candies is$0.20$ and the center of the middle figure is also at $0.20$ while the center of the third figure is at $0.40$ instead of $0.20$. Thus, it could be said that the second figure is appropriate for the sampling distribution of statistic.