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.

data for two batters

batter	at bats	hits	home runs
pujols	448	125	26

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

Explanation:

Step1: Calculate non - home - run hits for Jeter

Non - home - run hits for Jeter = Hits - Home Runs = 156 - 9=147.

Step2: Calculate expected points for Jeter per at - bat

Expected value formula for Jeter, $E(Jeter)=\frac{1\times147 + 4\times9}{488}=\frac{147+36}{488}=\frac{183}{488}\approx0.38$.

Step3: Calculate non - home - run hits for Pujols

Non - home - run hits for Pujols = Hits - Home Runs = 125 - 26 = 99.

Step4: Calculate expected points for Pujols per at - bat

Expected value formula for Pujols, $E(Pujols)=\frac{1\times99+4\times26}{448}=\frac{99 + 104}{448}=\frac{203}{448}\approx0.45$.

Answer:

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