Chapter 8, Problem 8.74RE

(a)

To determine

To describe how you would establish a correspondence between boxes of cereal that do and do not contain a dollar bill and numbers from Table B.

Explanation of Solution

  $\begin{array}{l}\text{Given: A dollar bill in every 20th box}\text{.}\\ \text{If you would have20 boxes, then you would expect one of them to contain the dollar bill}\text{.}\\ \text{You should then assign 1 value to the dollar bill and the 19 other values to no dollar bill}\text{.}\\ \text{Dollar Bill: Number 01}\\ \text{No Dollar bill: Numbers 02 to 20}\\ \text{We need to select a row from table B}\text{. Select the first 2 digit number from the row}\text{. If the}\\ \text{number is 01, then a dollar bill was obtained from the box}\text{. If the number is between 02 and}\\ \text{20, then no dollar bill was obtained from the box}\text{. If another number was selected ignore the}\\ \text{number and select the next 2 digit number}\text{.}\end{array}$

(b)

To determine

To describe how would you use your calculator to stimulate buying boxes of cheerios and checking the dollar bills.

Explanation of Solution

  $\begin{array}{l}\text{Given: A dollar bill in every 20th box}\text{.}\\ \text{If you would have20 boxes, then you would expect one of them to contain the dollar bill}\text{.}\\ \text{You should then assign 1 value to the dollar bill and the 19 other values to no dollar bill}\text{.}\\ \text{Dollar Bill: Number 01}\\ \text{No Dollar bill: Numbers 02 to 20}\\ \text{We generate such a box by using the following command for a Ti83-84 calculator:}\\ randInt(1,20)\end{array}$

(c)

To determine

To carry out stimulation to answer Mae Lee’s question.

Explanation of Solution

  $\begin{array}{l}\text{You will keep buying boxes until you obtain the first box with a dollar bill}\text{.}\\ \text{You make such a stimulation 25 times and record the number of boxes needed}\\ \text{until you bought the first box with a dollar bill:}\\ 29,8,51,7,27,1,5,2,15,39,8,8,17,73,27,3,19,25,8,41,1,2,6,16,2\\ \text{You then estimate number of boxes needed to obtain a one dollar bill as the mean}\\ \text{of the values}\text{. The mean is:}\\ \overline{x}=\frac{29+8+51+\mathrm{....}+6+16+2}{25}\\ =\frac{440}{25}\\ =17.6\\ \text{Thus the expected number of boxes needed until the first prize is 17}\text{.6}\text{.}\end{array}$