Question

derek jeter challenges albert pujols to a batting battle. each will earn 1 point for a hit other than a home run and 4 points for a home run in each round. which player should you back given the statistics in the table below? note that home runs are included as hits in the table.

batter	at bats	hits	home runs
pujols	448	125	26

e(jeter) = 0.38 and e(pujols) = 0.45, so back pujols
e(jeter) = 0.39 and e(pujols) = 0.51, so back pujols
e(jeter) = 0.34 and e(pujols) = 0.34, so it doesnt matter who you back
e(jeter) = 1.22 and e(pujols) = 0.94, so back jeter

Explanation:

Step1: Calculate Jeter's points

Non - home - run hits for Jeter are \(156 - 9=147\). Points from non - home - run hits are \(147\times1\), and points from home runs are \(9\times4\). Total points \(E(Jeter)=\frac{147\times1 + 9\times4}{480}=\frac{147+36}{480}=\frac{183}{480}=0.38125\approx0.38\).

Step2: Calculate Pujols's points

Non - home - run hits for Pujols are \(125 - 26 = 99\). Points from non - home - run hits are \(99\times1\), and points from home runs are \(26\times4\). Total points \(E(Pujols)=\frac{99\times1+26\times4}{448}=\frac{99 + 104}{448}=\frac{203}{448}\approx0.453\approx0.45\).

Answer:

E(Jeter) = 0.38 and E(Pujols) = 0.45, so back Pujols