Chapter 18, Problem 10E

To determine

To explain is this an unusually large proportion of green M&M’s.

Answer to Problem 10E

The expected proportion of green M&M’s is not the unusual.

Explanation of Solution

In the question, the candy company claims that $10\%$ of the M&M’s it produces are green. Suppose that the candies are packed at random in small bags. Then, the class of elementary school opens the bags and count the proportion that are green candies. Now, in a really large bag of M&M’s the student found $500$ candies and $12\%$ of them are green. Thus, now let us first find the mean and the standard deviation of this as:

  $\begin{array}{l}\mu =p=0.1\\ \sigma =\sqrt{\frac{pq}{n}}\\ =\sqrt{\frac{0.1(0.9)}{500}}\\ =0.01342\end{array}$

Thus, the z -score will be as:

  $\begin{array}{l}z=\frac{0.12-0.1}{0.01342}\\ =1.49\end{array}$

Thus, we can say that this proportion of M&M’s is about $1.49$ standard deviation above the expected proportion which is not the unusual.