Madison enjoys the game of golf. He knows that he will one-putt a green 15% of the time, two-putt 20% of the time, three-putt 35% of the time, and four-putt 30% of the time. Find the expected value for the number of putts Madison will need on any given green. Make sure to write down the entire equation that you used to solve this problem.

Answer:2.8 putts in average on any given greenStep-by-step explanation:To calculate how many putts Madison will need on any given green, we need to calculate the weighted average of his putts.We use a global sample of 100 puts and factor in the fact he had a one-putt performance 15% of the time, two-putts 20% of the time and so on.So, the calculation goes like this:[tex]\frac{1 * 15 + 2 * 20 + 3 * 35 + 4 * 30}{100}  = \frac{280}{100}  = 2.8[/tex]So, he'll need an average of 2.8 putts in average on any given green.Which makes sense since 65% of the time, he needs 3 putts or more on the green.