Question

Pamela is a leading server on her volleyball team. On average she serves at 8:44% of the time. She attempts 25 serves in her next game, how many aces would you expect her to have

Answer 1

She should be expected to have 2.11 aces.

Explanation:

I suppose there was a small typing mistake. It should be: On average she gets an ace of 8.44% of her serves.

Then

For each serve, there are only two possible outcomes. Either there is an ace, or there is not. The probability of there being an ace in a serve is independent of other serves. So we use the binomial probability distribution to solve this question.

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`

She gets an ace of 8.44% of her serves.

This means that
`p = 0.0844`

She attemps 25 serves:

This means that
`n = 25`

How many aces would you expect her to have

`E(X) = np = 25*0.0844 = 2.11`

She should be expected to have 2.11 aces.