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# Probability & Stats I MATH 370

WCU

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This 4 page Class Notes was uploaded by Alphonso Thompson on Thursday October 29, 2015. The Class Notes belongs to MATH 370 at Western Carolina University taught by Erin McNelis in Fall. Since its upload, it has received 9 views. For similar materials see /class/230959/math-370-western-carolina-university in Mathematics (M) at Western Carolina University.

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Date Created: 10/29/15

MATH 370 Probability amp Statistics I Probability Distributions Means and Standard Deviations for Discrete Random Variables PLNKOThe Puce ls nght Game Description A contestant IS shown four small pnzes For each pnze he or she sees two ohglts bu n the couect last digit For each small item guessed couectly the contestant Wins a chip Bob gives contestant a free chip JLBL fox playlrg the game so ve chips can be ealneol The contestant chmbs to the top of the Pllnko boalol see picture below and ohops the chips one at a time he pegs senol the chip bouncing all over the board until they lanol m slots xepxesentlrg money amounts a bottom The slots ale from left to zlght 100 500 1000 00 010000 00 1000 500 0100 After all the chips have oboppeol the contestant Wins whatever money he or she has ealneol to that point m m m m m m t l 4 5 l s 7 a The Pllnko board has 12 levels If you start from Slot 5 for example you neeol 6 left bounces and s xlght bounces to hit the 010000 slot at the bottom Simulating Dropping the Plinko Chip 1 You can simulate one drop with the random integer function by using randInt 0 1 12 STU gt L1 on the Tl 83 Note randInt is found under the MATH gt PRB menu option 5 If each 0 counts as a left bounce and each 1 as a right bounce the calculator creates 12 values randomly of either 1 or 0 and stores them in List 1 to Tally and record the total number of right bounces This can be recorded as sumL1 from the home screen note the sum function is found under the LIST gt MATH menu option number 03 To nd your location at the bottom of the Plinko board use the conversion table below which accounts for re ections off the wall The table assumes you drop the Plinko chip from Slot 5 of right bounces winnings 10000 0 4 8 12 a 1000 1 3 9 11 a 500 2 10 a 100 5 7 A 0 4 Repeat steps 1 3 ve times Record your results in the table below Plinko Chip of right bounces amount you win 2 3 4 5 TOTAL WlNNlNGS Probabilities 1 Record the results of your ve chips along with those of your classmates in the table below where z is the amount of your winnings from each Plinko chip Frequency 2 Change these frequencies into relative frequencies probabilities for your experimental results Rel Freq probability 03 F U a Now calculate the standard deviation for your simulation probabilities and for the true7 Compare your results to the true probability values for z x l 0 100 500 1000 1000 pzl3961024 331024 1161024 2481024 2311024 Why are the simulation results not identical to the true probability values Use your simulation data from before to calculate the expected winnings from one Plinko chip Use the table of true probability values to calculate the same expected value 7 probabilities Label them as as and 71quot for Simulation and True results Changing Starting Slots What happens if you drop the chip from Slot 4 The table below gives you this information Note this is a different distribution than when we dropped the chip from Slot 5 of right bounces77 winnings 7 a 10000 1 5 9 a 1000 2 4 10 12 a 500 3 11 a 100 0 6 8 a 0 7 7 The table below indicates the probability distribution for Plinko if you drop a chip from Slot 4 rather than Slot 5 x 0 100 500 1000 1000 pz 3551024 581024 1571024 2561024 1981024 1 Calculate the expected value of this probability distribution 2 Calculate the standard deviation 3 Which slot wins you more money in the long run Slot 4 or Slot 5 Explain 4 Which slot yield less variability Slot 4 or Slot 5 Explain

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