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:

$\sigma=\sqrt{n \times p \times q}$

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

$=\sqrt{n\times p\times(p-1)}$

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

$=\sqrt{21\times0.2\times(1-0.2)}$

$=\sqrt{21\times0.2\times0.8}$

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