Question

15% of Americans are known to be Walmart-aholics. They only shop at Walmart. What is the probability that exactly 9 in a group of 50 are Walmart-aholics? Calculate using:

a. Binomial

b. Poisson Approximation

c. Normal Approximation

Answer 1

a)

Let X denote the number of Americans known to be Walmart-aholics. Then

Required probability =

b)

Using Poisson approximation to Binomial distribution, we have,

Required probability =

c)

Using Normal approximation to Binomial distribution, we have,

Required probability =

{Due to continuity correction}