Question

miguel cabrera has had 369 at bats, and he has 127 hits and 21 home runs (note: the home runs are included in the hits data.) if he is challenged to a batting battle, what is the expected score of each at bat if he earns 1 point for each hit that is not a home run and 5 points for each home run?
0 0.36
0 0.43
0 0.57
0 0.63

Explanation:

Step1: Calculate non - home - run hits

The number of non - home - run hits is the total number of hits minus the number of home runs. So, the number of non - home - run hits is $127−21 = 106$.

Step2: Calculate total points

The total points from non - home - run hits is the number of non - home - run hits times 1 point per non - home - run hit, and the total points from home runs is the number of home runs times 5 points per home run. The total points $P=106\times1 + 21\times5=106 + 105=211$.

Step3: Calculate expected score per at - bat

The expected score per at - bat is the total points divided by the number of at - bats. So, the expected score per at - bat $E=\frac{211}{369}\approx0.57$.

Answer:

0.57