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1. Suppose that Li is playing a game. On each turn Li either gets or loses points. Let Y be the number of points Li gets on a turn. The pdf of Y is given below. Use the table to answer the following questions. a. Find the probability that Li gains points (Y > 0). b. Find the expected value or mean of Y. c. If Li's goal is to obtain points and she can play the game for many turns, should she play the game? Why? d. Find the standard deviation of Y. e. Find the probability that Y is within one standard deviation of its mean. Table 8.1: Game PDF 2. Some of Neil's donuts are filled, with crme or jelly for example. At any given time, there are many donuts in the donut shop (over 1000). From past experience, we estimate that 40% of the donuts made are filled. Suppose a customer orders a dozen assorted donuts and the employee randomly selects those dozen donuts. Answer the following questions. a. What is the probability that there are exactly 6 filled donuts in the dozen? . What is the probability that there are at most 5 filled donuts in the dozen? What is the probability that there are more than 5 filled donuts in the dozen? . What is the probability that there are at least 5 filled donuts in the dozen? What is the probability that there are between 3.5 and 8.5 filled donuts in the dozen? maon o 3. The weights of newborn black bear cubs are uniformly distributed with minimum of 255 and maximum of 305 grams. Suppose that a random newborn cub is selected. a. Find the probability that the newborn cub weighs less than 295 grams. Find the probability that the newborn cub weighs more than 270 grams. c. Find the probability that a newborn cub weighs more than 280 grams given it weighs more than 270 grams. d. Find the probability that a newborn cub weighs more than 290 grams given it weighs less than 300 grams. e. Find the 90" percentile of newborn cub weights