Questions: a. Explain how you would conduct a simulation using the random number table provided below to estimate the distribution of the number of prize winners each week. b. Perform your simulation three times. (That is, run three trials of your simulation.) Start at the leftmost digit in the first row of the table and move across. Make your procedure clear so that someone can follow what you did. You must do this by marking directly on or above the table. Report the number of winners in each of your three trials.

\(\boxed{\begin{array}{c} \begin{array}{c} \bigtriangleup \\ \text{Explanation of the Simulation} \\ \bigcirc \\ \text{Assign Numbers} \\ \bigodot \\ \text{Assign each coupon a number from 1 to 50, corresponding to its order of distribution.} \\ \bigcirc \\ \text{Read Random Numbers} \\ \bigodot \\ \text{Read two-digit numbers from the random number table, moving sequentially across the rows. If a number is 00, 51, 52, ..., 99, ignore it and move to the next two-digit number.} \\ \bigcirc \\ \text{Simulate Drawing Coupons} \\ \bigodot \\ \text{Each two-digit number between 01 and 50 represents a coupon number drawn by the radio station.} \\ \bigcirc \\ \text{Determine Cash Value} \\ \bigodot \\ \text{Determine the cash value of the selected coupon based on the following: Coupons 1-5: \$200, Coupons 6-20: \$100, Coupons 21-50: \$50.} \\ \bigcirc \\ \text{Calculate Total Awarded} \\ \bigodot \\ \text{Keep a running total of the cash values of the drawn coupons.} \\ \bigcirc \\ \text{Stop Condition} \\ \bigodot \\ \text{Stop drawing coupons when the total amount awarded equals or exceeds \$300.} \\ \bigcirc \\ \text{Record Number of Winners} \\ \bigodot \\ \text{Record the number of coupons drawn (i.e., the number of "winners") in that trial.} \\ \bigcirc \\ \text{Repeat} \\ \bigodot \\ \text{Repeat steps 2-7 many times (e.g., 100 or more trials) to obtain a distribution of the number of winners.} \\ \bigcirc \\ \text{Analyze Distribution} \\ \bigodot \\ \text{Analyze the distribution of the number of winners to estimate the typical number of winners and the variability in the number of winners each week.} \\ \star \\ \text{Explanation of the Simulation Completed} \\ \end{array} \\ \begin{array}{c} \bigtriangleup \\ \text{Simulation (Three Trials)} \\ \bigcirc \\ \text{Trial 1} \\ \bigodot \\ \text{72 - Invalid, 74 - Invalid, 91 - Invalid, 33 - Coupon 33 (\$50) - Total: \$50, 47 - Coupon 47 (\$50) - Total: \$100, 65 - Invalid, 03 - Coupon 3 (\$200) - Total: \$300, Stop.} \\ \bigcirc \\ \text{Trial 2} \\ \bigodot \\ \text{02 - Coupon 2 (\$200) - Total: \$200, 61 - Invalid, 28 - Coupon 28 (\$50) - Total: \$250, 49 - Coupon 49 (\$50) - Total: \$300, Stop.} \\ \bigcirc \\ \text{Trial 3} \\ \bigodot \\ \text{06 - Coupon 6 (\$100) - Total: \$100, 70 - Invalid, 29 - Coupon 29 (\$50) - Total: \$150, 04 - Coupon 4 (\$200) - Total: \$350, Stop.} \\ \star \\ \text{Simulation Results: Trial 1: 3 winners, Trial 2: 2 winners, Trial 3: 2 winners} \\ \end{array} \\ \begin{array}{c} \smiley \\ \text{Explanation of the Simulation Completed} \\ \text{Simulation Results: Trial 1: 3 winners, Trial 2: 2 winners, Trial 3: 2 winners} \\ \end{array} \end{array}}\)