Final answer:
To calculate the probability of Mark having at least 5 hits in his next 7 at-bats, we can use the binomial distribution.
Step-by-step explanation:
To find the probability that Mark will have at least 5 hits in his next 7 at-bats, we can use the binomial distribution. The formula for the probability of k successes in n trials is P(X=k) = (n choose k) * p^k * (1-p)^(n-k), where p is the probability of success and (n choose k) is the binomial coefficient. In this case, p is Mark's batting average, which is 0.21, and n is 7. We want to find the probability of having 5 or more hits, so we need to calculate P(X=5) + P(X=6) + P(X=7).
P(X=5) = (7 choose 5) * 0.21^5 * (1-0.21)^(7-5)
P(X=6) = (7 choose 6) * 0.21^6 * (1-0.21)^(7-6)
P(X=7) = (7 choose 7) * 0.21^7 * (1-0.21)^(7-7)
Adding up these probabilities will give us the total probability of having at least 5 hits in the next 7 at-bats.