Question

Past records indicate that the probability of online retail orders
that turn out to be fraudulent is 0.08. Suppose that, on a given
day, 20 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?

Answer 1

From the past records, 20 online retail orders are placed and the probability of online retail orders that turn out to be fraudulentis 0.08 Let X be the random variable indicates that the number of online retail or ders that turn out to be fraudulent, is follows binomial distributi on That is, X ~ Binomial (20, 0.08) The probability mass functi on is x 1s positive integer , P(X=x)-120 ( 0.08) (1-0.08 )20-x , x=0,1,2, ,20 (a) To find Mean and stan dard deviation of the number of online retail or ders that trun out to be fraudulent. Mean -np 20x0.0816 Vari ance np(1-p) 20x0.08x (1-0.08) 1.472 Stan dard deviation Variance 1472 -1.21326 (b) To find the probability that zero online retail orders will turn out to be fraudulent P(X = 0) = (0.08)0(1-0.08)"-0 0.081-0.08 1) (1) X (0.92 10. 18869 (c) To find the probability that one online retail orders will turn out to be fraudulent 20-1 0.08) (1-0.08 20x0.08x(092) 0.32816 (d) To find the probability that two or more online retail orders will turn out to be fraudulent. P(X2 2)-1- P(X <2) (0.08) (1-0.08)°+ 1[0.18869+0.32816] 1-[0.51685) = 10.48315