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,      μ=np

    Variance of X,     σ 2 =npq

    Standard deviation of X,      σ= 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 7 respectively, find the value of p and of n.

Solution:
Mean=90 np=90 Standard deviation=3 7 npq =3 7 npq=9( 7 ) Square both sides npq=63 ( np )q=63 90q=63 q= 7 10 p=1 7 10 = 3 10 From np=90, n( 3 10 )=90 n=300