Chapter 12, Problem AP4.3CPT

To determine

To find out at least how much the heaviest $30\%$ of these bananas weigh.

Answer to Problem AP4.3CPT

Option (d) is the correct option.

Explanation of Solution

It is given that:

  $\begin{array}{l}\mu =116\\ \sigma =9\end{array}$

The cutoff value for the heaviest $30\%$ is the same as the cut off value for the lower $100\%-30\%=70\%$ weighs.

Now, we will find the z-score that corresponds with a probability $70\%$ in the normal probability. Thus, the z-score is:

  $\begin{array}{l}z=0.50+0.02\\ =0.52\end{array}$

Thus, we have,

  $\begin{array}{l}z=\frac{x-\mu }{\sigma }\\ =\frac{x-116}{9}\\ \Rightarrow \frac{x-116}{9}=0.52\\ \Rightarrow x-116=0.52(9)\\ \Rightarrow x=116+0.52(9)\\ \Rightarrow x=120.68\end{array}$

Thus, the heaviest $30\%$ of these bananas weigh at least $120.68$ g or approximately $121$ g.

Thus, option (d) is the correct option.