The Car Repair Ratings website provides consumer reviews and ratings for garages in the United States and Canada. The time customers wait for service to be completed is one of the categories rated. The following table provides a summary of the wait-time ratings (1 5 Slow/Delays; 10 5 Quick/On Time) for 40 randomly selected garages located in the province of Ontario, Canada (Car Repair Ratings website, November 14, 2012).

Wait-Time Number of

Rating Garages

1 ..........6

2 ..........2

3 ..........3

4 ..........2

5 ..........5

6 ..........2

7 ..........4

8 ..........5

9 ..........5

10 ..........6

a. Develop a probability distribution for x 5 wait-time rating.

b. Any garage that receives a wait-time rating of at least 9 is considered to provide outstanding service. If a consumer randomly selects one of the 40 garages for their next car service, what is the probability the garage selected will provide outstanding wait-time service?

c. What is the expected value and variance for x?

d. Suppose that 7 of the 40 garages reviewed were new car dealerships. Of the 7 new car dealerships, two were rated as providing outstanding wait-time service. Compare the likelihood of a new car dealership achieving an outstanding wait-time service rating as compared to other types of service providers.