ANSWER and EXPLANATION
(a) We want to find the range of values that Rachel can use to represent a treasure box that has a wand.
The chances of getting an amulet, a wand, or a ring all add up to 100.
This implies that from the number 1 to 100, 1 - 34 can represent a treasure box having an amulet.
In other words, the next 47 numbers can represent a treasure box having a wand i.e. 35 - 81.
Finally, the last 19 numbers can represent a treasure box having a ring i.e. 82 - 100.
Therefore, the range of values that Rachel can use to represent a treasure box having a wand is 35 - 81.
(b) To find the percentage of the treasure boxes that had a wand, find the number of random numbers that fall in the range of 35 - 81, divide by 10, and multiply by 100.
There are 8 simulated treasure boxes whose random number falls in the given range, hence, the percentage of boxes that had a wand is:
[tex]\begin{gathered} \frac{8}{10}*100 \\ \\ \Rightarrow80\% \end{gathered}[/tex]
That is the answer.
