Question

a) State two properties of a
i) Binomial experiment ii) Normal distribution
[6 Marks] [1 Mark]
[2 Marks] [2 Marks]
b) If the probability that an individual suffers a bad reaction from injection of a given serum is 0.001, use the Poisson law to calculate the probability that out of 2000 individuals
i) Exactly 3 individuals will suffer a bad reaction. [3 Marks] ii) More than 2 individuals will suffer a bad reaction.

Answer 1

(a)

(i) two properties of a Binomial experiment

Property 1: Binomial experiment consists of n independent trals, each having in just two outcomes

Property 2: Probability of success = p is the same in each trial

(ii) two properties of a Normal distribution

Property 1: Mean, median andmode areequal

Property 2: The curve issymmetricat the center.

(b)

(i)

Poisson Distribution

n = 2000

p = 0.001

Mean = = np = 2000 X 0.001 = 2

So,

Answer is:

0.1805

(ii)

P(X>2) = 1 -[ P(X = 0) + P(X=1) + P(X=2)]

Substituting, we get:

P(X>2) = 1 -[ P(X = 0) + P(X=1) + P(X=2)] = 1 - 0.6767 = 0.3233

So,

Answer is:

0.3233