Question

in a binomial distribution if n=6 and q=0.7 then mean?​

Answer 1

Answer:

If p is the probability of success and q is the probability of failure in a binomial trial, then the expected number of successes in n trials (i.e. the mean value of the binomial distribution) is. E(X) = μ = np. The variance of the binomial distribution is. V(X) = σ2 = npq.

Step-by-step explanation:

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Answer 2

Basic Concept Used :-

We know that,

In Binomial Distribution,

• n = number of trials

• p = probability of success

• q = probability of failure

• r = random variable associated with the experiment

Then,

• Mean of Binomial Distribution = n × p.

Also,

• p + q = 1

Let's solve the problem now!!!

Given that

• Number of trials, n = 6

• Probability of failure, q = 0.7

We know that

$\rm :\longmapsto\:p + q = 1$

$\rm :\longmapsto\:p + 0.7 = 1$

$\rm :\longmapsto\:p = 1 - 0.7$

$\bf\implies \:p = 0.3$

Now,

We have

• Number of trials, n = 6

• Probability of success, p = 0.3

So,

$\rm :\longmapsto\:Mean = n \times p$

$\rm :\longmapsto\:Mean = 6 \times 0.3$

$\green{\bf :\longmapsto\:Mean = 1.8}$

Additional Information :-

In Binomial Distribution,

$\boxed{ \sf \:variance \: = npq}$

$\boxed{ \sf \:Standard \: deviation \: = \sqrt{npq}}$

$\boxed{ \sf \:Mean > variance}$