b. [1 point} What is the average of the lti simulated spins? How does this value compare to your answer in part 2c? c. [1 point} Include the simulated probabilit3.r mass function AND the plot of the probabilittr mass function from Ft. For the probability mass function. you should include a table with the all possible outcomes and the proportion of times each outcome was spun [output from line 43 of the code}. d. [1 point} How different are the simulated probabilities to the theoretical probabilities in part 2? e. [1 point} Based on the plot are the least likely outcomes the same as it is in part 2a? f. [1 point} In general. what action will make the simulated "u'ElIIJEE more like the theoretical ones? Part 2: (11 palntsl Wheel of Fortune is a popular game show on Teleyision. Contestants spin a wheel and try to guess a correct letter from a word puzzle. If they guess correctly. they earn the dollar amount from the wheel. if they spin "bankrupt\" or \"lose a turn" they get nothing and can't play. To the right is an example of the wheel. Watch this yideo to see an example of someone Spinning the wheel. W 5: www. outuoeco watch?y= Py33 WBcl'fEl The outcome of a spin on the wheel is a discrete random yariaole. Consider K the dollar amount spun on the wheel, where Bankrupt and Lose a Turn = $0. and Free Play = 55m}. There are 24 wedges on the wheel. PMF for Spin Outcome 0 20 0.10 0.0D 0 300 350 400 450 500 550 600 700 900 900 The following table provides the probability mass function for X. Round values to 3 decimal places. X $0 $300 $350 $400 $450 $500 $550 $600 $700 $800 $900 |$5,000 Count 2 5 2 2 P(x) 0.083 0.208 0.042 0.083 0.042 0.125 0.042 0.125 0.042 0.083 0.083 0.042 a. (1 point) What is the least likely dollar amount? There may be more than one dollar amount considered "least likely". b. (1 point) How likely is it to spin and land on $600? C. (3 points) What is the average dollar amount? Show work! d. (3 points) Suppose a contestant spins the wheel three times, how likely is it they spin $600 each time? Show work! e. (3 points) Suppose a contestant spins the wheel three times, how likely is it they spin $600 at least one time? Show work!Part 3: (6 points) The PMF in Part 2 is based on probability theory. Do these probabilities stand up when a contestant actually spins the wheel? Go back to the Data Analysis #1 instructions page on Canvas, download the R script titled: Wheel_of Fortune_Spin_Script.R, open the file it will automatically open in R. You need R software on the computer to open the script window. Follow the instructions in the code then answer the following: a. (1 point) What value did you spin