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MAT 142 Problem Solving NAME: PS U6C: Problem Solving Binomial Probability On June 17, 20191, Boston Red Sox right fielder Mookie Betts has a batting average of 0.266 for the 2019 season. This average means he makes a base hit 26.6% of his times at bat. The Red Sox have a three game series with the Twins coming up. As lead-off batter, Mookie Betts bats about 4-5 times per game, he will have around 12 at bats if he plays each game. Use this information and binomial probability to determine the following: Show your thinking clearly, including how you set up the problems. a. P(Betts hits exactly 3 of the 12 times he is at bat): b. P(Betts hits exactly 6 of the 12 times he is at bat): c. P(Betts hits exactly 9 of the 12 times he is at bat): d. Which of the three scenarios in a, b, c has the highest probability? Why does this make sense? e. Find: P(Betts hits 2 or fewer of the 12 times he is at bat): Interesting Quote from Baseball Great Mickey Mantle: "During my 18 years I came to bat almost 10,000 times. I struck out about 1,700 times and walked maybe 1,800 times. You figure a ballplayer will average about 500 at bats a season. That means I played seven years without ever hitting the ball.&quot