Question

99 POINTS!

Find the standard deviation for the binomial distribution.

n=21; p=0.2

A) 1.83
B) 5.95
C) -0.58
D) 5.10

Answer 1

Standard deviation = √(n * p * q)

You are given n and p

q = 1 - p

q = 1 -0.2 = 0.8

Standard deviation = √(21 * 0.2 * 0.8)

=√3.36 = 1.83

The answer is A.

Answer 2

The standard deviation for a given binomial distribution
`n` and
`p` would be the following:

`\sigma=√(n * p * q)`

The variable
`q` is equivalent to
`(p-1)`

`=√(n* p*(p-1))`

Substitute the values of
`p` and
`n` into the equation

`=√(21*0.2*(1-0.2))`

`=√(21*0.2*0.8)`

Use a calculator to solve for this square root since it would be too hard and complicated to do by hand

`=1.83303027798...`

Round this to the nearest hundredths place since all answer choices are rounded like that

`=1.83`

Thus, the answer is choice A. Let me know if you need any clarifications, thanks!

~ Padoru