Twenty percent of the students in a class of 100 are planning to go to graduate school. The standard deviation of this binomial distribution is

For any binomial variable X having parameters n (total number of trials ) and p (probability of getting success in each event), the standard deviation is given by :-

[tex]\sigma=\sqrt{np(1-p)}[/tex]

As per given , we have

n= 100 , p= 20%=0.20

Then, the standard deviation of this binomial distribution is :

[tex]\sigma=\sqrt{100(0.20)(1-0.20)}\\\\=\sqrt{100(0.16)}=4[/tex]

Hence, the standard deviation of this binomial distribution is 4.

abidemiokin abidemiokin · Answer 2 · 2021-10-26T13:00:45+02:00

The standard deviation of this binomial distribution is 4 if twenty percent of the students in a class of 100 are planning to go to graduate school

The formula for finding the standard deviation of this binomial distribution is;

[tex]\sigma = \sqrt{np(1-p)}[/tex]

n is the sample size

p is the percentage of students in the class

Given the following parameters

n = 100

p = 20% = 0.2

Substitute the given parameters into the formula

[tex]\sigma = \sqrt{np(1-p)}\\\sigma = \sqrt{100(0.2)(1-0.2)}\\\sigma = \sqrt{20(0.8)}\\\sigma = \sqrt{16}\\\sigma = 4[/tex]

Hence the standard deviation of this binomial distribution is 4

Learn more here: https://brainly.com/question/15061321