Probability and hypothesis

1. Chapter 1 - Problem 18

The General Store at State University is an auxiliary bookstore located near the dormitories that sells supplies, toiletries, sweatshirts and t-shirts, magazines, packaged food items, and canned soft drinks and fruit drinks. The manager of the store has noticed that several pizza delivery services near campus make frequent deliveries. As such, the manager is considering selling pizza at the store. She could buy pre-made frozen pizzas and heat them in an oven. The cost of the oven and freezer would by $27,000. The frozen pizzas cost $3.75 each to buy from a distributor and to prepare (including labor and a box). To be competitive with the local delivery services, the manager believes she should sell the pizzas for $8.95 each. The manager needs to write up a proposal for the university's directory of auxiliary services.

a. Determine how many pizzas would have to be sold to break even.

b. If the General Store sells 20 pizzas per day, how many days would it take to break even?

c. The manager of the store anticipates that once the local pizza delivery services start losing business, they will react by cutting prices. If after a month (30 days) the manager has to lower the price of a pizza to $7.95 to keep demand at 20 pizzas per day, as she expects, what will the new break-even point be, and how long will it take the store to break even?

2. Chapter 1 - Problem 20

Annie McCoy, a student at Tech, plans to open a hot dog stand inside Tech's football stadium during home games. There are seven home games scheduled for the upcoming season. She must pay the athletic department a vendor's fee of $3,000 for the season. Her stand and other equipment will cost her $4,500 for the season. She estimates that each hot dog she sells will cost her $0.35. She has talked to friends at other universities who sell hot dogs at games. Based on their information and the athletic department's forecast that each game will sell out, she anticipates that she will sell approximately 2,000 hot dogs during each game.

What price should she charge for a hot dog in order to break even by the end of the season? Do part a of this problem only.

3. Chapter 2 - Problem 8

An automobile manufacturer has discovered that 20% of all the transmissions it installed in a particular style of truck one year are defective. It has contacted the owners of these vehicles and asked them to return their trucks to the dealer to check the transmission. The Friendly Auto Mart sold seven of these trucks and has two of the new transmissions in stock. What is the probability that the auto dealer will need to order more new transmissions?

4. Chapter 2 - Problem 14

A metropolitan school system consists of three districts - north, south, and central. The north district contains 25% of all students, the south district contains 40% of all students, and the central district contains 35%. A minimum competency test was given to all students. 10% of the north district students failed, 15% of the south district students failed, and 5% of the central district students failed. (Do b and c only)

a. DO NOT DO

b. Develop a joint probability table.

c. What is the probability that a student selected at random from anywhere in the school system failed the test?

5. Chapter 2 - Problem 26

The weight of bags of fertilizers is normally distributed with a mean of 50 pounds and a standard deviation of 6 pounds. What is the probability that a bag of fertilizer will weigh between 45 and 55 pounds?

6. Chapter 2 - Problem 36

The Palace Hotel believes its customers may be waiting too long for room service. The hotel operations manager knows that the time for room service orders is normally distributed and he samples 10 room service orders during a 3-day period and timed each (in minutes) as follows:

23 15 26 19 30 23 12 16 18 25

The operations manager believes that only 10% of the room services orders should take longer than 25 minutes if the hotel has good customer service. Does the hotel room service meet this goal?