Grades in a statistics course. North Carolina State University posts the gradedistributions for its courses online.4 Students in Statistics 302 in the Spring 2005semester received 45% As, 35% Bs, 16% Cs, 2% Ds, and 2% Fs. Choose aStatistics 302 student at random. To choose at random means to give everystudent the same chance to be chosen. The students grade on a four-point scale(with A = 4) is a discrete random variable X with this probability distribution:Value of X 01234Probability 0.02 0.02 0.16 0.35 0.45(a) Say in words what the meaning of P(X 3) is. What is this probability?(b) Write the event the student got a grade poorer than C in terms of values ofthe random variable X. What is the probability of this event?

Conditional Probability: probability of an event, given that another event has occurred P(A| B) is the probability of A, given that B has occurred P(A| B) is not the same as P(B|A) If events are independent then P(A)=P(A|B) and P(B)=P(B|A) A contingency table (two way table) is a visual representation of the relationships between the variable. They make probabilities easier to figure out. Levels...