1. (20 points) Probability Table

A marketing professional for a plumbing company asked 200 customers in three locations how they heard about his company.The resulting counts are given in the two-way table below.

Branch Location

Suppose that one of the customers is selected at random. Using this data set, find the following probabilities.

a.(4 points) The person learned about the company through an online ad.

P(Online Ad)= 23+32+14/200

= 0.345

b.(4 points) Given that the person learned by word of mouth, the person’s branch location is Chicago.

P(Word

c.(4 points) The person heard about the company through word of mouth or used services from the Miami location.

d.(4 points) Given that the person used services at the Chicago location, the person learned about the company through a newspaper ad.

e.(4 points) Let A be the event that the person learned about the company through word of mouth. Let B be the event that the person used services at the Atlanta location. Are A and B independent events? Explain.

• (20 points) Probability
  • (10 points) A car rental company has five sedans and four coupes available.The company wants to send three of its vehicles to a mechanic for preventative maintenance this week.
  • (10 points) West Buy sell electronic devices including TV sets. From historical data, the store believes that only 10% of the customers browsing for TV sets actually buy a set. On a given day 20 customers browsed for TV sets at a local West Buy store.
• (20 points) Discrete Random Variable: Probability Distribution

a.(5 points) How many different ways are there to select a group of three vehicles to send to the mechanic?

b.(5 points) If each car has an equal chance at being selected, what is the probability that the cars sent will include one sedan and two coupes?

a.(5 points) What is the probability that at least 4 customers buy a TV set?

b.(5 points) What is the average number of TV sets sold on this day?

A publisher wants to feature three of its authors on its website.It has five current authors; two write children’s books, and two write novels for adults.All are equally likely to be chosen.Let the random variable X = the number of children’s authors chosen, where x = 0, 1, 2.

a)(10 points) Construct the probability distribution of X.

b)(3 points) Find E(X).

c)(3 points) Find Var(X).

d)(4 points) To feature its authors, the company would incur a cost of $1000 for each children author, $1500 for each adult author and $2000 for a generic author. What is the expected cost incurred by the company to feature its authors?