1:33 PM Man April 'E' '3' L BTWEP 6 9 +5- Stat 2. Spring 222 Assignment 4 Name: SID: 2. In a gambling game. I roll two dice and win $1 if the sum of my two rolls is larger than T. I lose $1 if the sum of my two rolls is smaller than F. In any other cases, I don't lose or win anything. I am going to repeat this game ?2 times. {3.} Write your answers as simplied fractions: What is the chance I win $1 on a single play? What is the chance I lose $1 on a single play? What is the chance I don't win or lose any money on a single play? [In] Based on your answers to {a}, write down a box model for my net gain, including the values on the tickets in the box, the number of repeats of each ticket. and how many draws we will make wlth replacement from the box. to] Now make a box model for the number of times i win. including the 1Iralues on the tickets, the number of repeats of each ticket. and how many draws we will make with replacement from the hex. 1:16 PM Mon Apr 4 . . . 98% 5 O + : (a) (b) 0.00 0.02 0.04 0.06 0.08 0.00 0.02 0.04 0.06 0.08 0 20 40 60 80 100 -100 -50 0 50 100 150 200 0.06 (c) 0.12 (d) 0.04 0.08 0.02 0.04 0.00 0.00 10 20 30 40 20 30 40 0.12 (e) 0.012 (f) 0.08 0.008 0.04 0.004 0.00 0.000 10 20 30 40 -100 -50 50 100 150 200 10 V1:21 PM Mon Apr 4 ... 0 96% T O + : SID: Instructions: SHOW ALL YOUR WORK. Partial credit may be given, and full credit may NOT be given if work is not shown. You will need a calculator and the normal table to do this assignment. 1. I am playing a gambling game. On each play, I have a 20% chance of winning $12, a 20% chance of breaking even (not winning or losing any money), and 60% chance of losing $5. I play this game 200 times. (a) Write down the box model to represent this situation, including the values on the tickets, the number of repeats of each ticket, and how many draws we will make with replacement from the box. (b) The average of this box is and the SD of the box is (c) In 200 plays, my net gain (total amount won or lost) has an expected value of $ , with a standard error of $ (d) What is the chance that I come out ahead (have a positive net gain) after the 200 plays? Use the normal approximation to calculate this. % A 10 +1:16 PM Mon Apr 4 4? G) t 98%E}