Question

A baseball player has a lifetime batting average of 0.223. If, in a season, this player has 385 "at bats", what is the probability he gets 103 or more hits? Probability of 103 or more hits = ______

Answer 1

To find the probability that the baseball player gets 103 or more hits in a season, we need to use the concept of a binomial distribution. Calculate the probability of getting exactly 103 hits using the binomial distribution formula and then calculate the cumulative probability of getting 103 or more hits by adding up the individual probabilities.

Step-by-step explanation:

To find the probability that the baseball player gets 103 or more hits in a season, we need to use the concept of a binomial distribution. First, we need to calculate the probability of getting exactly 103 hits. The formula for calculating the probability of getting k hits in n at-bats with a batting average of p is:

P(X = k) = C(n, k) * p^k * (1-p)^(n-k)

Substituting the values, we get:

P(X = 103) = C(385, 103) * 0.223^103 * (1-0.223)^(385-103)

Now, to find the probability of getting 103 or more hits, we need to calculate the cumulative probability:

P(X >= 103) = P(X = 103) + P(X = 104) + ... + P(X = 385)

Calculate each individual probability using the formula mentioned above and add them up to get the final probability.