Explained: "For a binomial distribution mean is 6 and..."

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Answered question

2021-10-01

For a binomial distribution mean is 6 and variance is 2. Find the

P (X = 4)

.
a) 0.1024
b) 0.0012
c) 0.1768
d) 0.1345
e) 0.8976

Arnold Odonnell

Skilled2021-10-02Added 109 answers

Step 1
Given :
For a binomial distribution mean is 6 and variance is 2.
Also,
The mean of the distribution

(μ x)

is equal to

n \cdot P = 6

The variance

(σ_{x}^{2}) i s n \cdot p \cdot (1 - p) = 2

Step 2
We can put the value of

n \cdot p

in variance equation ,then

n \cdot p \cdot (1 - p) = 2

6 \cdot (1 - p) = 2

1 - p = \frac{1}{3}

p = \frac{2}{3}

Hence,

n = \frac{6}{\frac{2}{3}} = 9

The full binomial probability formula with the binomial coefficient is:

P (X) = \frac{n!}{X! (n - X)!} \cdot p^{X} \cdot {(1 - p)}^{n - X}

Computing

P (X = 4)

P (4) = \frac{9!}{4! (9 - 4)!} \cdot {0.6667}^{4} \cdot {(1 - 0.6667)}^{9 - 4}

P (X = 4) = 0.10239 \approx 0.1024

Correct Option is:
a) 0.1024.

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