The random variable k has a geometric distribution with mean 16. which of the following is closest to the standard deviation of random variable k ?

a. 0.0625
b. 0.9375
c. 4
d. 15.49
e. 240

The standard deviation of random variable K is 15.49 and this can be determined by using the formula of mean and standard deviation.

Given :

The random variable K has a geometric distribution with a mean 16.

The mean is given by the formula:

Substitute the value of in the above formula in order to determine the value of 'p'.

p = 0.0625

The standard deviation is given by the formula:

Now, substitute the value of p in the above formula in order to determine the standard deviation.

Therefore, the correct option is d).

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d. 15.49

Step-by-step explanation:

Given : The random variable K has a geometric distribution with mean 16.

Formula for Mean and standard deviation in geometric distribution:

   (1)

  (2), where p is the probability of success in each trial.

Since  (Given)

Then from (1) ,

Put value of p in (2),

Hence, the standard deviation of random variable K is closest to 15.49.

Therefore , the correct answer is d. 15.49 .

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