Theoretical Distribution Overview: This project is 2 separate Stats Labs. The data has been provided for you (crossed off sections have already been completed but are still listed so you can understand the process). It is data collected from a previous term. These are excellent applications to the material covered. Build the theoretical PDF chart based on the distribution in the Procedure section. Chapter 4 - Discrete Distribution (Playing Card Experiment) Remember that x is the number of diamonds that each student drew. So for the table in #1, 2 students drew 10 cards, with replacement, and drew zero diamonds. Procedure - The experimental procedure for empirical data is to pick one card from a deck of shuffled cards For the theoretical distribution, if x = 0 we are trying to find the theoretical probability of a student drawing 10 cards, with replacement, and drawing zero diamond cards. 0 11 1 The theoretical probability of picking a diamond from a deck is Shuffle a deck of cards. Pick one card from it. Record whether it was a diamond or not a diamond. Put the card back and reshuffle. Do this a total of ten times. Record the number of diamonds picked. 2. Let X = number of diamonds. Theoretically, X-BL Organize the Data 14 115 16 P(x) 0.05631= 5.63% 0.18771= 18.77% 0.28157= 28.16% 0.25028= 25.03% 0.14600= 14.6% 0.05840= 5.84% 0.01622= 1.62% 0.00309= 0.3% 0.0003= 0.03% 0.00002= 0.002% 0.000000953= 9.53*10^-7)% 3. Record the number of diamonds picked for your class with playing cards in Table 4.16. Then calculate the relative frequency 17 8 9 x Relative Frequency 0 Frequency 2 6 10 1 2 7 See my work done by hand below for further explanation: 113 4 9 4 2 15 16 4 Boomial Probability Distribution Sanalso use E Easy Caictato where: n=13 PQ 03.Qm* 7 1 8 0 19 0 p=.25 10 0 X Table 4.16 4. Calculate the following. Round your answer to the nearest hundredth. a. X= b. S = 3 4 5 60 7 a= l-p:\-.25.75 % Total # of Success lolo (.25). (.75)0.0560-5.6% 100.6.25) - (75) 0.187 = 18.7% C. (25) (75) = 0.281 = 28.1% Hala (.25.1757 0.250 = 25% oly 1.25 1.750 = 0. 146 = 14.42 10.1.255. (35 0.058 = 58%. Lolu - 1.25) 4. 1.750 0.016 lo (25) (.75 0.003 = 0.3% Co (25) . (75) 0.0003 - 0.032 Fiala. (25) 25' 6.00002 0.002% LC (25 9.53X10-7 9 5. Calculate the following for the theoretical distribution. Round your answer to the nearest hundredth a. V = b. o = Using the Data NOTE: RF = relative frequency 6. Use the table from the Theoretical Distribution section to calculate the following answers. Round your answers to four decimal places. a. P(x = 3) = b. P(1