Respuesta :
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:
[tex]\mu=\dfrac{1}{p}[/tex] (1)
[tex]\sigma=\dfrac{\sqrt{1-p}}{p}[/tex] (2), where p is the probability of success in each trial.
Since [tex]\mu=16[/tex] (Given)
Then from (1) ,
[tex]\dfrac{1}{p}=16\\\Rightarrow\ p=\dfrac{1}{16}=0.0625[/tex]
Put value of p in (2),
[tex]\sigma=\dfrac{\sqrt{1-0.0625}}{0.0625}=\dfrac{\sqrt{0.9375}}{0.0625}[/tex]
[tex]=\dfrac{0.968245836552}{0.0625}[/tex]
[tex]=15.4919333848\approx15.49[/tex]
Hence, the standard deviation of random variable K is closest to 15.49.
Therefore , the correct answer is d. 15.49 .
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:
[tex]\mu = \dfrac{1}{p}[/tex]
Substitute the value of [tex]\mu[/tex] in the above formula in order to determine the value of 'p'.
[tex]16 = \dfrac{1}{p}[/tex]
p = 0.0625
The standard deviation is given by the formula:
[tex]\rm \sigma =\dfrac{ \sqrt{{1-p}}}{p}[/tex]
Now, substitute the value of p in the above formula in order to determine the standard deviation.
[tex]\rm \sigma =\dfrac{ \sqrt{1-0.0625}}{0.0625}[/tex]
[tex]\rm \sigma = \dfrac{\sqrt{0.9375} }{0.0625}[/tex]
[tex]\sigma = 15.49[/tex]
Therefore, the correct option is d).
For more information, refer to the link given below:
https://brainly.com/question/17921485
