Question: The weight of parcels received at a warehouse loading dock is normally distributed with a mean of 300 lbs. and a standard deviation of 50 lbs. The weight of a parcel is independent of the weight of any other parcel.

a) (10 points) Consider three parcels selected randomly at the dock. What is the probability that exactly two of the three parcels weigh more than 400 lbs. each?

b) (10 points) Parcels that weigh less than 400 lbs. do not get damaged; those weighing more than 400 lbs have a probability of 0.1 of getting damaged in handling at the dock. Whether a package is damaged or not is independent of any other package. What is the probability that none of three randomly selected parcels will be damaged?