Angry that their grades on the Operations Management midterm weren’t as high as they wanted, Raul, Chulin, Tyler, Chris, Nuo, and David decide to get revenge on Mike by egging his car in the parking lot. From where they’re standing, each egg they throw has a probability of 0.6 of hitting Mike’s car. If everyone in the group throws an egg at the same time, what is the probability that…
a. … exactly four of the eggs will hit Mike’s car?
b. … at least four of the eggs will hit Mike’s car?
c. … no more than four of the eggs will hit Mike’s car?
d. Rongkai is also mad about his grade on the midterm, and decides to join in on the egging as well. He is standing 75 feet directly behind the rear bumper of Mike’s car. The distance Rongkai can throw an egg is normally distributed with mean 80 feet and standard deviation 5 feet. Mike happens to be walking by just as Rongkai launches an egg at his car. If Mike’s car is 15 feet long, what is the probability that Rongkai will miss hitting it with the egg he just threw (and therefore still have a chance to pass Operations Management)?