Respuesta :
Answer:
The mean, variance, and standard deviation of the binomial distribution are 10, 8, and 2.83 respectively.
Step-by-step explanation:
We have to find the mean, variance, and standard deviation of the binomial distribution with the given values of n and p, i.e; n = 50 p = 0.2.
Let X = binomial random variable
So, X ~ Binom(n = 50, p = 0.2)
Now, the mean of the binomial distribution is given by;
Mean of X, E(X) = n [tex]\times[/tex] p
= 50 [tex]\times[/tex] 0.2 = 10
Now, the variance of the binomial distribution is given by;
Variance of X, V(X) = n [tex]\times[/tex] p [tex]\times[/tex] (1 - p)
= 50 [tex]\times[/tex] 0.2 [tex]\times[/tex] (1 - 0.2)
= 10 [tex]\times[/tex] 0.8 = 8
Also, the standard deviation of the binomial distribution is given by;
Standard deviation of X, S.D.(X) = [tex]\sqrt{\text{n} \times \text{p} \times (1 - \text{p})}[/tex]
= [tex]\sqrt{\text{50} \times \text{0.2} \times (1 - \text{0.2})}[/tex]
= [tex]\sqrt{8}[/tex] = 2.83
