Question

According to the NCAA, 12.8% of high school men's lacrosse players will end up playing at the collegiate level. If 20 male high school lacrosse payers are selected at random, find the probability that exactly four of them will play at the college lacrosse. Express your answer as a probability between C and 1 and round to three decimal places.​

Answer 1

This question involves using the binomial distribution.

Let X be the number of male high school lacrosse players who will play at the college level out of the 20 selected players . We can model X as a binomial random variable with parameters n=20 and p=0.128, where p is the probability of success (i.e., a player going on to play at the college level).

The probability of exactly 4 players playing at the college level is given by the formula:

P(X=4) = (20 choose 4) * (0.128)^4 * (1-0.128)^(20-4)

Using a calculator, we can evaluate this expression to find:

P(X=4) = 0.155

Therefore, the probability that exactly four of the 20 male high school lacrosse players selected at random will end up playing at the college level is 0.155, or between C and 1 (inclusive).

Note that we rounded to three decimal places as requested .