Question

A certain insecticide kills 70 % of all insects in laboratory experiments. A sample of 11 insects is exposed to the insecticide in a particular experiment. What is the probability that less than 4 insects will die? Round your answer to four decimal places.

Answer 1

p = probability that certain insecticide kills all Insects = 0.70.

n = sample size =11.

X - no of insects die on action of insecticide

X follows binomial distribution with parameters n= 11 and p = 0.70 hence X takes values 0,1,2,3,... Up to 11

Probability mass function is

P ( X=x) = nCx * p^x * (1-p)^(n-x) ,x=0,1,2.......11

=0 otherwise

To find probability that less than 4 insects will die

i.e P ( X<4) = P (X=0)+ P ( X=1) + P ( X=2) +

P (X =3)

= (11C0 * 0.7^0 * 0.3^11)+

(11C1* 0.7^1*0.3^10)+ (11C2* 0.7^2 *0.3^9) +(11C3 * 0.7^3 *0.3^8)

=0.00000177+0.00004546+0.00053+0.0037

=0.004277

Required Probability is 0.0042