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:
[tex]E(X) = np[/tex]
The Stomping Elephants volleyball team plays 30 matches in a week-long tournament.
This means that [tex]n = 30[/tex]
On average, they win 4 out of every 6 matches.
This means that [tex]p = \frac{4}{6} = \frac{2}{3}[/tex]
What is the mean for the number of matches that they win in the tournament?
[tex]E(X) = np = 30\frac{2}{3} = 20[/tex]
The mean for the number of matches that they win in the tournament is 20.
