# 8.1b Mean, Variance and Standard Deviation of a Binomial Distribution

8.1b Mean, Variance and Standard Deviation of a Binomial Distribution

2. Determine the mean, variance and standard deviation of binomial distribution

If X is a binomial discrete random variable such that   X~B (n, p),
then

Mean of X,     $\overline{)\mu =np}$

Variance of X,    $\overline{){\sigma }^{2}=npq}$

Standard deviation of X,     $\overline{)\sigma =\sqrt{npq}}$

Example 1:
A Football club organises a practice session for trainees on scoring goals from penalty kicks. Each trainee takes 8 penalty kicks. The probability that a trainee scores a goal from a penalty kick is p. After the session, it is found that the mean number of goals for a trainee is 7.2.
Find the value of p.

Solution:
Mean = np
np = 7.2
8p = 7.2
p = 0.9

Example 2:
X is a binomial random variable such that X ~ B (n, p). If its mean and standard deviation are 90 and  $3\sqrt{7}$ respectively, find the value of p and of n.

Solution: