Application 5.6 What's a good batting average? In baseball, a player's batting average is the proportion of times that the player gets a hit out of his total number of times at bat. Suppose we select a Major League Baseball player at random. The random variable X = the player's batting average can be modeled by a normal distribution with mean = 0.261 and standard deviation = 0.034. 1. Fill in the values on the normal curve. 050 -2 SD -150 SO 2 SD 3 SD 2. Find the probability of a batting average greater than 0.329. 3. Find the probability of a batting average between 0.193 and 0.295. I Suppose we convert the randomly selected player's batting average to a z-score. Use Stapplet to find each of the following. Draw a standard normal distribution with the desired area shaded in each case. 4. What's the probability that the z-score is between -0.58 and 1.79? 5. 45% of batting averages will have a z-score below what value?