Chapter 5 Test 1. The probability distribution below is for the random variable X = the number of credits taken by a randomly selected first-year student at a large state university Credits 14 15 16 17 Probability | 0.05 0.65 0.20 0.10 (a) Show that the probability distribution of X is (b) Make a histogram of the probability distribution. valid. (1pt) Describe its shape. (1pt) (c) Express the event "taking at least 16 credits" in terms of X and find its probability. (2pts) 2. Classify each of the following random variables as discrete or continuous. Explain. (1 pt) (a) H = the number of homework problems assigned by your statistics teacher on a randomly selected class day (b) T = winning time in the men's 100-meter dash at a randomly selected international track meet 3. In a lake 30% of the fish are thrown back because they are too small. Consider catching 20 fish from the lake. Assume that the fish you caught can be considered a random sample from the very large number of fish in the lake. Let Y = the number of fish that you throw back because they are too small. (a) Explain how Y can be considered a binomial random variable. (2 pts) (b) Find My. Interpret the My. (1pt) (c) Find oy. Interpret the oy. (1 pt)