Problem 6E

One out of every 5000 individuals in a population carries a certain defective gene. A random sample of 1000 individuals is studied.

a. What is the probability that exactly one of the sample individuals carries the gene?

b. What is the probability that none of the sample individuals carries the gene?

c. What is the probability that more than two of the sample individuals carry the gene?

d. What is the mean of the number of sample individuals that carry the gene?

e. What is the standard deviation of the number of sample individuals that carry the gene?

Solution

Step 1 of 6

Here given one out of every 5000 individual in a population carries a certain defective gene

So, p=1/5000

=0.0002

The sample size 1000

So, n=1000

Let X is no.of individuals carries the gene

Here XB(1000,0.0002)

Since ‘n’ is large and ‘p’ is small

The Binomial distribution will be converted to poisson distribution

The pmf of poisson distribution is P(X)=, X=0,1,2,..............

So, =np

=1000(0.0002)

=0.2

Hence XPoisson (0.2)