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?
0.36
0.43
0.57
0.63

Explanation:

Step1: Calculate points from non - home - run hits

The number of non - home - run hits is $127 - 21=106$. Each non - home - run hit gives 1 point, so the points from non - home - run hits is $106\times1 = 106$ points.

Step2: Calculate points from home runs

Each home run gives 5 points and there are 21 home runs. So the points from home runs is $21\times5=105$ points.

Step3: Calculate total points

The total points is the sum of points from non - home - run hits and home runs, so $106 + 105=211$ points.

Step4: 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 is $\frac{211}{369}\approx0.57$.

Answer:

0.57