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AP Statistics 7.02 Means and Variances of Random Variables Directions: Complete the assignment. Clearly label each answer. (30 points) 1. Find the average, money won/loss for the Camp Wannahockaloogi (raffle ticket on next page) using the plan outlined below. (20 points: 10 points for the table, 5 points for item g, 5 points for item h). a. Make a table with five columns labeling one column "Event" (How much money can be won). b. Label another column "x", this is the random variable; it is the winning MINUS the cost of the ticket. c. Label the next column "Frequency", this is the number of winners for each prize. d. Label the next column "P(x)". This is the probability for each event. e. Label the last "x * P(x)". This column will be used to calculate the expected value (Average). f. Calculate the product "x * P(x)" by multiplying the random variable, "x", by its corresponding probability, "P(x)". g. Find the sum of this column. Interpret this amount. h. Verify your answer Event x Frequency P(x) X*P(x) Win underwater treasure chest ($100 value) $95 1 1/100 $95/100 Win goggles ($50 value) $45 1 1/100 $45/100 Win bumper sticker ($10 value) $5 1 1/100 $5/100 Lose ($0) -$5 97 97/100 -$485/100 Total net -340/100 The sum of all x*P(x) shows that ticket buyers lose an average of $340/100, while the camp makes a profit of $340/100 per ticket sold, so if all 100 tickets were sold, the charity would have made a profit of $340.
Prize value: $100 + $50 + $10 =$160 Profit = revenue – spending on prizes: (100tickets*$5 per ticket) = $340 This calculated profit is the expected value in profits. Camp Wannahockaloogi Summer Raffle 2014 100 Tickets @ $5 each 1 st Prize – Underwater Treasure Chest ($100 value) 2 nd Prize – Goggles etched with the address P. Sherman, 42 Wallaby Way ($50 value) 3 rd Prize – “Fish are Friends, not Food” bumper sticker ($10 value) Drawing to be held May 4, 2014 2. An AP Statistics teacher is desperately rummaging around her box of AAA batteries trying to find 2 working batteries for a student’s graphing calculator. The teacher has 10 batteries, 3 of which are dead. The teacher randomly selects two batteries. a. Create a probability model (values for a random variable and corresponding probabilities) for the number of good batteries (4 points): P(two bad) = P(x=0)=3/10 * 2/9 = 1/15 P(one good and one bad) = P(x=1) = 3/10 * 7/9 + 7/10*3/9 = 7/15 P(two good) = P(x=2) = 7/10*6/9 = 7/15 b. What is the expected number of good batteries the teacher selects? (3 points): Expected number = x*P(x=0) + x*P(x=1) + x*P(x=2) Expected number = 0*1/15 + 1*7/15 + 2*7/15 = 7/5 c. What is the standard deviation? (3 points):
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