An entomologist studying a certain species of large moth has found that the number of wing beats ...

An entomologist studying a certain species of large moth has found that the number of wing beats per second (while in flight) for this species ranges from 6 to 10. He finds that the species uses 6 beats/second 5% of the time, 7 beats/second 10% of the time, 8 beats/second 65% of the time, and 9 beats/second 12% of the time.

a) Construct a probability model for the random variable wing beats per second. Verify that it’s a true probability distribution.

b) If X is the random variable for # wings/second, then find the following. (Show your work.)

P(X < 8) =

P(X ≥ 7) = 

P(X > 7) =