Question

The probability that a tennis set will go to a tiebreaker is 13%. In 120 randomly selected tennis sets, what is the mean and the standard deviation of the number of tiebreakers

Answer 1

`\mu = 15.6`

`\sigma =3.684`

Explanation:

Given

`p =13\%`

`n = 120`

Solving (a): The mean

This is calculated as:

`\mu = np`

So, we have:

`\mu = 13\% * 120`

`\mu = 15.6`

Solving (b): The standard deviation

This is calculated as:

`\sigma = \sqrt{\mu * (1 - p)`

So, we have:

`\sigma = \sqrt{15.6 * (1 - 13\%)`

`\sigma = \sqrt{15.6 * 0.87`

`\sigma =\sqrt{ 13.572`

`\sigma =3.684`