Question

In a binomial distribution number of trial is 6 and the probability of success is 0.4 then variance is

Answer 1

$\large\underline{\sf{Solution-}}$

In Binomial Distribution,

• n represents number of independent trials

• p represents probability of success

• q represents probability of failure

Given that,

• Number of trials, n = 6

• Probability of success, p = 0.4

We know that,

p + q = 1

On substituting the value of p = 0.4, we get

0.4 + q = 1

q = 1 - 0.4

⟹ q = 0.6

Now,

We have,

• n = 6

• p = 0.4

• q = 0.6

We know,

Variance of Binomial Distribution is given by

$\rm :\longmapsto\:Variance = npq$

$\rm \: \: = \: \: 6 \times 0.4 \times 0.6$

$\rm \: \: = \: \: 1.44$

$\rm \: \: = \: \: \dfrac{36}{25}$

$\bf\implies \:Variance = \dfrac{36}{25}$

Additional Information :-

In Binomial Distribution,

• Mean of Binomial Distribution = np

• Mean of Binomial Distribution > Variance