It is claimed that 15% of the ducks in a particular region have patent schistosome infection. Suppose that seven ducks are selected at random. Let X equal the number of ducks that are infected.

(a) Assuming independence, how is X distributed?

(b) Find (i) P(X ≥ 2), (ii) P(X = 1), and (iii) P(X ≤ 3).

Answer :

Step 1 of 2:

It is claimed that 15% of the ducks in a particular region patent schistosome infection.

Here sample each bird is a bernoulli trials with success defined as detecting the infection.

Then the probability duck is infected is

P(duck is infected)= 15%

P(duck is infected)= 15/100

P(duck is infected)= 0.15

The random variable x denotes the number of infected ducks in the sample of size n=7.

Therefore x has binomial distribution b(n , p)

We know that n=7 and p = 0.15

Xb(7,0.15)

a).

Here we are assuming independence,X distributed is

P(X)=; x = 0,1,2,...,7