The National Highway Trac Safety Administration (NHTSA) crash-tests new car models to determine how well they protect the driver and front-seat passenger in a head-on collision. The NHTSA has developed a star scoring system for the frontal crash test, with results ranging from one star to ve stars. The more stars in the rating, the better the level of crash protection in a head-on collision. The star ratings for some car models are summarized in the following table:

Star rating 2 3 4 5

Frequency 2 16 60 22

(a) Calculate the mean of the star ratings.

(b) Calculate the median of the star ratings.

(c) Suppose that insurance premium is estimated according to the star rating. For the standard insurance plan, the premium schedule is as follows. Calculate the expected insurance premium when a car model is randomly selected.

Star rating 2 3 4 5

Insurance premium $500 $200 $120 $100