Question

in baseball, a 0.300 hitter gets a hit in 30% of times at bat. when a baseball player hits 0.300, fans tend to be impressed. typical major leaguers bat about 500 times a season and hit about 0.260. a hitter's successive tries seem to be independent. could a typical major leaguer hit 0.300 just by chance?

Answer 1

To determine if a typical major leaguer could hit 0.300 just by chance, we can calculate the probability using the binomial probability formula. The probability is extremely low, indicating it is highly unlikely for a typical major leaguer to hit 0.300 just by chance. Therefore, a batting average of 0.300 is impressive.

Step-by-step explanation:

To determine if a typical major leaguer could hit 0.300 just by chance, we can calculate the probability. Let's assume that a typical major leaguer has a batting average of 0.260 and gets 500 times at bat in a season. We can use the binomial probability formula to calculate the probability of getting exactly 150 hits (0.300 batting average).

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

Where:
n = number of trials (at bats)
k = number of successes (hits)
p = probability of success (batting average)

In this case, n = 500, k = 150, and p = 0.260. Plugging these values into the formula, we can calculate the probability.

P(X = 150) = C(500, 150) * 0.260^150 * (1 - 0.260)^(500 - 150)

This probability is extremely low, indicating that it is highly unlikely for a typical major leaguer to hit 0.300 just by chance. Therefore, a batting average of 0.300 is impressive.