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3. An experiment has the probability distribution given in the table below. X 1 2 3 4 P(X = X) 0.5 0.1 0.3 0.1 a) (3 points) What is the probability that a single randomly-chosen value of X is less than 2.5? Calculate out to a numeric answer. You must show all of your steps to receive full credit. b) (7 points) A sample of size 49 is randomly selected from the population. What is the probability that the sample mean is less than 2.5? Calculate out to a numeric answer. You must show all of your steps to receive full credit. NOTE: Insert Math Equation does not have a way to insert the notation for sample mean. If you are referring to the random variable, type in X-bar. If you are referring to the calculated value, type in x-bar