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Question

If the sum of the mean and variance of B.D. for 5 trails is 1.8, the binomial distribution is

A
(0.8+0.2)5
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B
(0.2+0.8)5
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C
(0.8+0.2)10
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D
(0.2+0.8)10
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Solution

The correct option is A (0.8+0.2)5

A binomial distribution is characterized by 2 parameters:

n - number of trials

p - probability of success in 1 trial

We already know n=5, we need to find p.

Mean of a binomial distribution is given by

mean =np

Variance is given by

variance =np(1p)

mean+variance=1.8

5p+5p(1p)=1.8

5p210p+1.8=0

p2(1.8+0.2)p+0.36=0 [Dividing by 5 then using factor]

(p0.2)(p1.8)=0

p=0.2 or p=1.8(nonconsiderable) because p is probability so it can not be greater than 1.

So the binomial distribution is n=5,p=0.2.


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