Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 12
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# In a Binomial Distribution, the Probability of Getting Success is 1/4 and Standard Deviation is 3. Then, Its Mean is (A) 6 (B) 8 (C) 12 (D) 10 - Mathematics

#### Question

In a binomial distribution, the probability of getting success is 1/4 and standard deviation is 3. Then, its mean is

• 6

• 8

• 12

• 10

#### Solution

12

$p = \frac{1}{4}$
$\therefore q = 1 - \frac{1}{4} = \frac{3}{4}$
$\text{ Standard deviation }= 3$
$\Rightarrow\text{ Variance } = 3^2 = 9$
$\text{ Or npq } = 9$
$\Rightarrow np = \frac{9}{q}$
$= \frac{36}{3}$
$= 12$
$\text{ Therefore, the mean of the given binomial distribution is 12 } .$

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