Past records indicate that the probability of online retail orders that turn out
ID: 3327804 • Letter: P
Question
Past records indicate that the probability of online retail orders that turn out to be fraudulent is 0.04. Suppose that, on a given day, 18 online retail orders are placed. Assume that the number of online retail orders that turn out to be fraudulent is distributed as a binomial random variable.
a. What are the mean and standard deviation of the number of online retail orders that turn out to be fraudulent?
b. What is the probability that zero online retail orders will turn out to be fraudulent?
c. What is the probability that one online retail order will turn out to be fraudulent?
d. What is the probability that two or more online retail orders will turn out to be fraudulent?
Explanation / Answer
This is a binomial distribution with p=0.04 and n=18
a) Mean is n*p=18*0.04=0.72
Variance is n*p*(1-p)=18*0.04*(1-0.04)=0.6912 , thus standard deviation is sqrt(0.6912)=0.8314
b) P(x=0)=18C0*(0.04)^0*(0.72)*18=0.4796
c) P(x=1)=18C0*(0.04)^1*(0.72)*17=0.3597
d) P(x>=2)=1-P(x<2)=1-(P(x=0)+P(x=1))=1-(0.4796+0.3597)=0.1607