SM230 Probability

Sections 2003/3002

Test 2

NAME: _________________________

DATE: _______17 Mar 97___________

You may use your calculators. Specify which program you used and with what parameters. For example, BCDF(p=4/9,N=17,X=3). Also, circle your final answer and give 4 decimal places. The setting is a cruise ship between Miami and the Bahamas.

  1. You board a cruise ship in Miami for a weeks cruise in the Caribbean Sea (Kathie Lee Gifford is NOT onboard). 69% of the passengers onboard are retirees.
  1. If the table assignments for dinner are made randomly, what is the probability that an 8 person table has fewer than four retirees assigned?
  2. What capacity table should we request to be 80% sure of getting more than four retirees assigned?
  1. The cruise director is organizing a 10 person scuba diving expedition and goes from stateroom to stateroom to get participants. 30% of the passengers are scuba qualified.
  1. What is the probability that the cruise director will ask more than 25 passengers before finding 10 qualified to participate in the expedition?
  2. How many passengers should be asked to be 90% sure you have asked enough to find the 10 required?
  1. The breakfast buffet contains 25 Danish pastry and 17 bagels. You ask for room service to deliver a mixture of 6 for your brunch.
  1. What is the chance you receive more than 2 Danish and more than 1 bagel?
  2. How many (total) should you request to be 75% sure of getting three or more bagels?
  1. During the early morning hours, passengers arrive at the swimming pool at a rate of 3 per hour. Three swimmers are required before anyone can enter the pool (no lifeguard is on station).
  1. If you arrive at 0700 and no one is at the pool, what is the probability you will wait more than 15 minutes for another swimmer to arrive?
  2. What is the probability that fewer than three swimmers will be present in 45 minutes?
  3. Will it take less than 35 minutes before you can begin swimming?
  1. The ship's casino has slot machines that payoff at a rate of once every 2 hours.
  1. What is the probability that a guest who plays the slots for 90 minutes will win at least one jackpot?
  2. How long should a guest play the slots to be 85% sure of winning a jackpot?
  3. If seven guests play the slots for 90 minutes each, what is the probability that more than three will win at least one jackpot?