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Question

In a binomial distribution the probability of getting a success is 14 and standard deviation is 3, then its mean is


A

6

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B

8

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C

10

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D

12

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Solution

The correct option is D

12


Explanation for the correct option.

Find the mean of the binomial distribution.

In a binomial distribution, n is the number of trials, p is the probability of success, and q is the probability of failure.

It is given that probability of getting a success is 14, so p=14.

Now the value of q can be found using p+q=1.

p+q=114+q=1q=1-14q=34

So the probability of getting a failure is q=34.

Variance is the square of standard deviation. As the standard deviation is 3. So the variance is 32=9.

Now, variance is given by npq. So equate it with 9 and put the values of p and q to find the value of n.

npq=9n×14×34=9p=14,q=34n=9×163n=48

Now the mean of the distribution is given as np. So substitute the values and find the mean.

Mean=np=48×14n=48,p=14=12

So the mean of the given binomial distribution is 12.

Hence, the correct option is D.


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