MATH245

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Data Assignment #3 ( 100 pts) Each student should have unique answers for Q1 and Q 2: this is not a group assignment !1. Design your own game , similar to the example in the course notes on page 89 . and the lotto example in the document in CANVAS/FILES called RANDOM VARIABLES.Do not use a die roll for your game. Some ideas could use cards, spinners , or a similar device .( 10 pts) a. Describe the scenario, and provide the probability distribution for the payout scheme. Your game should have a negative expected value ( favors the house not the player) and at least one positive payout. So you have to think about this a bit to make sure it works out correctly.(15 pts) b. Based on your probability distribution, compute the mean payout per play and the standard deviation.( 10 pts) c. Simulate 10000 plays of your game in Statcrunch:Create a column called “game”, and enter values that generate the correct the probability of each outcome. For example, the example in course notes p. 89, I would enter game11- 1.50- 1.50-1.752.5Then click Data / Sample . Choose “game” as variable. Change the sample size to 10000 and check SAMPLE WITH REPLACEMENT . Click Compute .Use Statcrunch to Compute the mean and standard deviation of your 10000 simulated plays.Copy and paste the summary stats showing n , mean , and standard deviation.
2. Create a Binomial Probability Experiment. Recall that this means the experiment must have n independent success/failure trials with the probability of success (p) and failure (q) the same each time . a. (20 pts) Describe your scenario here. Define a Binomial Random Variable X.Make sure you clearly define what a success is, and what n, p , and q are for your scenario. There is no specific value of x here, since this is a general scenario not associated with a particular number of successes.OFF LIMITS: coin flips, die rolls, any example I have used in class.b. ( 10 pts) Illustrate your scenario, either by a photo, original art, clip art , or any other illustration .( 10 pts) c. YOU WILL ONLY WORK ONE OF THE FOLLOWING OPTIONS BASED ON YOUR SCENARIO.If your value of p is less than or equal to .5 , Use Statcrunch / Stat/ Calculators/ Binomial to find the probability that 2/5 OR MORE of your trials result in a success .If your value of p is greater than .5 , Use Statcrunch / Stat/ Calculators/ Binomial to find the probability that at 3/5 OR LESS of your trials result in a success For example , if n= 50 and p = .6 , you would find P(X <= 50*3/5 ) = P( X <= 30 ) . For example , if n= 50 and p = .4 , you would find P(X >= 50*2/5 ) = P( X >= 20 ) . Round up to next whole number if n *2/5 or n * 3/5 is not a whole number.(10 pts) d. Compute the mean and standard deviation for your scenario by hand using formulas mean = np and std dev. = sqrt( npq), ( 15 pts) e. Use Statcrunch to simulate 10000 rounds your experiment:select Data/ Simulate / Binomial. Enter 10000 for rows, and 1 for columns. Enter the values for n and p for your scenario .Click Compute Create a relative frequency histogram of your results. Show it here:Approximate the answer to part c by placing the cursor over the graph for the appropriate classes and added up the relative frequencies .

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