Question

One out of every 5000 individuals in a population carries a certain defective gene. A random sample of 1000 individuals is studied. What is the probability that exactly one of the sample individuals carries the gene? What is the probability that none of the sample individuals carries the gene? What is the probability that more than two of the sample individuals carry the gene? What is the mean of the number of sample individuals that carry the gene?

Answer 1

0.8187,0.00115,0.20

Explanation:

Given that one out of 5000 individuals in a population carries a certain defective gene.

Hence in the sample of 1000, we find X no of those carrying defective gene will follow a Poisson distribution with mean
`= 1/5 = 0.2`

a)

the probability that none of the sample individuals carries the gene

`=P(x=0)\\= 0.8187`

b) the probability that more than two of the sample individuals carry the gene

=
`P(X>2) = 0.00115`

c) the mean of the number of sample individuals that carry the gene

0.20