Ne lake Period Y Formative: Random Variables, Expected Value, & Binomial Distribu During a season, a basketball player has an 85% success rate in shooting from the free throw lin In one match the player has po shots from the free throw line, Find the probability that the play successful with: a. All 20 shots [2) 0, 389 b. At least 18 shots 0 243 o. No more than 15 shots [2] 0. 182 A policeman inspected the safety tires on cars passing through a checkpoint. The number of tires X which needed replacing on each car followed the probability distribution below, P(X - 2) 0.68 0.2 0.06 0.02 a. Find the value of k. [1] b. Find the mode of the distribution. [2] c. Find the median of the distribution. [2] d. Find P(X 2 2). [2] e. Find P(X $ 3). [2] f. Find P(X > 0). [2] g. Find the expected value E(x) for the distribution. [2]