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

Answer:

$\mu = 15.6$

$\sigma =3.684$

Step-by-step 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:

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

$\sigma = \sqrt{15.6 * 0.87$

$\sigma =\sqrt{ 13.572$

$\sigma =3.684$