Math 1342 Signature Assignment

Signature Assignment Important Instructions to the Student: 1.All explanations must be typed. The supporting math work must be neat and suitable for copying or scanning to insert into this document. The final document should be saved and submitted as a single .pdf, .doc, or .rtf file. 2. Submit your assignment via Blackboard by the deadline established by your instructor. A charity organization hosts a raffle drawing at a fund raising event. The organization sells 2500 tickets at a price of $8 each. Winning tickets are randomly selected, with 30 prizes of $100, 10 prizes of $500, and 1 grand prize of $8000. Suppose you buy one ticket. Let the random variable X represent your net gain from playing the game once (remember that the net gain should include the cost of the ticket). 1. Use the table below to help you construct a probability distribution for all of the possible values of X and their probabilities. 2. Find the mean/expected value of X. (Round to two decimal places.) E ( x )= 7092 ( 1 / 2500 )+ 492 ( 10 / 2500 )+ 92 ( 30 / 2500 )− 8 ( 2459 / 2500 ) E ( x ) =− 1.60 Using the mean/expected value formula for the probability distribution the value of X is -1.60. 3. In complete sentences, describe the interpretation of what your value from #2 represents in the context of the raffle. From using the expected value formula, the value of X being -1.60 is the average net gain of buying one raffle ticket. Meaning when participating in the raffle multiple times the losses average to -$1.60. 4. If you were to play in such a raffle 100 times, what is the expected net gain? X = 100 ( − 1.60 ) X =− $ 160 The expected net gain from participating in the raffle 100 times is -$160. 5. Would you choose to buy a ticket for the raffle? (Your response should be a short paragraph, written in complete sentences, to explain why or why not.) I would not choose to buy a ticket for the raffle. Even if a person wins or loses there is still a X (Net Gain) Probability $-8 2459/2500 $92 30/2500 $492 10/2500 $7092 1/2500