Question

1. Complaints about an Internet brokerage firm occur at a rate of 3 per day. The number of complaints appears to be Poisson distributed.

A. Find the probability that the firm receives 3 or more complaints in a 2-day period.

2. In the United States, voters who are neither Democrat nor Republican are called Independent. It is believed that 13% of voters are Independent. A survey asked 15 people to identify themselves as Democrat, Republican, or Independent.

A. What is the probability that more than 3 people are Independent?

Answer 1

1)

Since , the rate of complaints about an Internet brokerage firm occur at a 3 per day.

Let , X be the number of complaints.

Here , X has a Poisson distribution with parameter =3 per day

Therefore , the probability mass function of X is ,

; ,

= 0 ; otherwise

Now , we want to find the probability that the firm receives 3 or more complaints in a 2-day period.

Theerfore , =2*3=6 per 2 day period.

Now ,

; From Poisson distribution table

Therefore , the probability that the firm receives 3 or more complaints in a 2-day period is 0.9380.

2)

Let , X be the number of the independent people

Here , X has binomial distribution with parameter n=15 and p=0.13

Therefore , the probability mass function of X is ,

; x=0,1,2,.........,n and q=1-p

=0 ; otherwise

Now , we want to find the probability that more than 3 people are Independent.

Therefore , the probability that more than 3 people are Independent is 0.1204