In a binomial distribution the probability of getting a success i… - Vidyadip

MCQ

In a binomial distribution the probability of getting a success is $\frac{{1}}{{4}}$ and standard deviation is $3$, then its mean is

A
$6$
B
$8$
✓
$12$
D
$10$

✓

Answer

Correct option: C.

$12$

c
(c) Probability of success $p = \frac{1}{4}$

Probability of unsuccess $q = \frac{3}{4}$

Mean $= np$

Standard deviation $= \sqrt {{\rm{Variance }}} $

$ \Rightarrow $ Variance $= 9$

$⇒ npq = 9 ⇒ n.\,\frac{1}{4}.\,\frac{3}{4} = 9 ⇒ n = 48$

Mean $ = np$ $ = \frac{1}{4} \times 48 = 12$.

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