1. Mustafa gets a job as a stock clerk at the local Cost-Mart store. One of his duties is to unpack the produce from the shipping crates as they arrive at Cost-Mart and place it on the shelves. Mustafa has observed that half of the crates he unpacks hold 50 pounds of produce, 30% of the crates that arrive hold 35 pounds, and the other 20% of the crates hold 60 pounds. A new crate of produce has just arrived for Mustafa to unpack. Calculate the expected value, variance, and standard deviation of the weight of the crate.
2. Jessica is talking on the phone with Siyuan as she’s waiting for customers at her nail salon. Siyuan tells Jessica that she’d like to treat herself to a manicure after surviving that brutal Operations Management midterm. “I actually don’t have any customers right now,” says Jessica. “Why don’t you come on over right now?”
Siyuan thinks about it a moment, and says, “Yeah, I think I will. I should be there in about twenty minutes.”
“Twenty minutes?” Jessica replies. “If it’ll take you that long, I might already have a customer by the time you get here. I usually get an average of four customers an hour.”
a. If Siyuan leaves for Jessica’s nail salon right now, what is the probability that exactly three customers will arrive while she’s driving there? (Hint: What distribution should you use if you only know the average number of arrivals in a given time interval?)
b. What is the probability that Siyuan will have to wait in line when she gets there?