Question

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

Answer 1

Answer: 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:

$\mu=\dfrac{1}{p}$    (1)

$\sigma=\dfrac{\sqrt{1-p}}{p}$   (2), where p is the probability of success in each trial.

Since $\mu=16$  (Given)

Then from (1) ,

$\dfrac{1}{p}=16\\\Rightarrow\ p=\dfrac{1}{16}=0.0625$

Put value of p in (2),

$\sigma=\dfrac{\sqrt{1-0.0625}}{0.0625}=\dfrac{\sqrt{0.9375}}{0.0625}$  

$=\dfrac{0.968245836552}{0.0625}$

$=15.4919333848\approx15.49$

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

Therefore , the correct answer is d. 15.49 .