Question

Let X be a binomial random variable with n = 400 trials and probability of success p = 0.01. Then the probability distribution of X can be approximated by

Select one:

a. a Hypergeometric distribution with N = 8000,  n = 400,  M = 4.    

b. a Poisson distribution with mean 4.

c. an exponential distribution with mean 4.

d. another binomial distribution with  n = 800, p = 0.02

e.
a normal distribution with men 40 and variance 3.96.

Answer 1

We have given that , X follows a Binomial distribution with n= 400 and success probability p=0.01.

We can use a Normal distribution as a limiting distribution of binomial , but when n> 20 and p<= 0.05

That is,when np< 10 , then Poisson approximation to binomial is appropriate.

Here, np = 4 ie , np<10

So, we approximate Binomial to Poisson distribution with mean, = n* p = 400* 0.01 = 4

So correct option is b) a Poisson distribution with mean =4.