Question

miguel cabrera has had 398 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 3 points for each home run?

Explanation:

Step1: Calculate the probability of non - home run hit

The total number of at - bats is \(127 + 21=148\). The number of non - home run hits is \(127\). The probability of a non - home run hit \(P(\text{non - HR})=\frac{127}{148}\).

Step2: Calculate the probability of home run hit

The number of home runs is \(21\). The probability of a home run hit \(P(\text{HR})=\frac{21}{148}\).

Step3: Calculate the expected value

The expected value formula is \(E(X)=x_1P(x_1)+x_2P(x_2)\). Here, \(x_1 = 1\) (points for non - home run) and \(x_2 = 5\) (points for home run).

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Answer:

\(1.57\)