Question

Consider the following binomial experiment. Suppose that 81% of mice that consumed a certain poison will die from it. If 1,700 mice consume the poison, what is the standard deviation of the number of mice that will die from it?
a) 3.23
b) 261.63
c) 13.77
d) 1,377
e) 16.17
f) None of the above.

Answer 1

Answer: e) 16.17

Step-by-step explanation:

In Binomial distribution ,

The formula to find the standard deviation is given by :-

$\sigma=\sqrt{np(1-p)}$ , where p= population proportion.

n= sample size.

Given : The proportion of mice that consumed a certain poison will die from it : p= 81% =0.81

The sample size = n= 1700

Then, the standard deviation of the number of mice that will die from it is given by :-

$\sigma=\sqrt{1700(0.81)(1-0.81)}$

$\sigma=\sqrt{1700(0.81)(0.19)}$

$\sigma=\sqrt{261.63}=16.1749806801\approx16.17$

Hence, the standard deviation of the number of mice that will die from it= 16.17