In 13 professional football seasons from 1999 to 2011, kicker David Akers recorded the following results for field goal attempts of various distances.

Use the implied percentages as probabilities to answer the following questions:
(a) A made field goal scores 3 points. What is the expected value (in points scored) if Akers attempts a 45-yard kick?
(b) During a game, Akers attempts kicks of 27, 38, and 51 yards. What is the expected contribution of these kicks to the Eagles€™ score in the game? What assumptions do you need?
(c) His team can allow Akers to attempt a 37-yard kick. They can also go for a first down. If they go for a first down and fail, they score nothing. If they make the first down, half of the time Akers will get a chance to kick from less than 30 yards and half of the time they score a touchdown (worth 7 points). They have a 35% chance to make the first down. What should they do?

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Attempts Distance 0-19 20-29 30-39 40-49 50+ Made 112 123 128 41 109 2 89