(b) Determine the appropriate degrees of freedom for this test. (0) Sketch a (very) crude graph of a probability density function that has the general shape for a X2 distribution, and shade in the region Whose area would be the pvalue for this test. (d) For a X2 distribution with the appropriate degrees of freedom for this test, you happen to know that P(X 2 7.815) = 0.05. Determine the appropriate outcome for the GoodnessofFit test on this data set. 1. You've landed an unusual job testing the performance of a prize wheel used for a televised game show. The wheel has been designed to deliver various outcomes with known probability, but the wheel is also a mechanical device that might drift from this objective over time. Your job is to see whether the wheel needs adjustment. You spin the wheel 200 times, and see these outcomes versus expectation: Observed Expected Game Over Small Prize 120 l Major Prize l 30 Grand Prize 15 Table Q1: Game show wheel outcomes, observed counts after 200 trials versus expected counts. (a) Determine the X2 score for a Goodness-ofFit test on this data set