Question

The Stomping Elephants volleyball team plays 30 matches in a week-long tournament. On average, they win 4 out of every 6 matches. What is the mean for the number of matches that they win in the tournament?

Answer 1

Answer:

The mean for the number of matches that they win in the tournament is 20.

Step-by-step explanation:

For each match, there are only two possible outcomes. Either they win, or they do not. The probability of winning a match is independent from other matches. So we use the binomial probability distribution to solve this problem.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

The expected value of the binomial distribution is:

$E(X) = np$

The Stomping Elephants volleyball team plays 30 matches in a week-long tournament.

This means that $n = 30$

On average, they win 4 out of every 6 matches.

This means that $p = \frac{4}{6} = \frac{2}{3}$

What is the mean for the number of matches that they win in the tournament?

$E(X) = np = 30\frac{2}{3} = 20$

The mean for the number of matches that they win in the tournament is 20.