Mathematics, 14.01.2020 00:31 katlyn10289

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

Answers: 2

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Answers

Answer from: MaeWolfe

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:

$\mu = \dfrac{1}{p}$

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

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

p = 0.0625

The standard deviation is given by the formula:

$\rm \sigma =\dfrac{ \sqrt{{1-p}}}{p}$

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

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

$\rm \sigma = \dfrac{\sqrt{0.9375} }{0.0625}$

$\sigma = 15.49$

Therefore, the correct option is d).

For more information, refer to the link given below:

link

Answer from: gobbler80

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 .

Answer from: Quest

the line of

Answer from: Quest

the number of possible outcomes that do not show a 1 on the first spinner and show the number 4 on the second spinner is 2.

spinner 1 spinner 2

1 1

1 2

1 3

1 4

2 1

2 2

2 3

2 4 = not 1, and 4

3 1

3 2

3 3

3 4 = not 1, and 4

only 2 outcomes have passed the given condition.

step-by-step explanation:

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