Question

A. 12% of Americans are known to be Walmart-aholics. They only shop at Walmart. What is the probability that exactly 7 in a group of 50 are Walmart-aholics? Calculate using:

a. Binomial

b. Poisson Approximation

c. Normal Approximation

B. using the same approach as in the previous question. What is the probability the number of trials it takes to get the first success is a multiple of 4, i.e P(X= 4, 8, 12, 16,….). Use p= 0.25

Answer 1

a) The distribution given here is:

Therefore the required probability here is computed as:

Therefore 0.1467 is the required probability here.

b) Here, we are given the mean rate as np = 50*0.12 = 6

Therefore the distribution could be approximated here as:

Therefore the required probability is now computed as:

Therefore 0.1377 is the required probability here.

c) The mean and standard deviation are first computed as:

Therefore the required probability is computed as:

( due to the binomial correction )

Converting it to standard normal scores, we get:

Getting it from the standard normal tables, we get:

Therefore 0.1570 is the required probability here.