I. Introduction
Arrowmark Vending has the contract to supply pizza at football games for a university. The operations manager, Tom Kealey, faces the challenge of determining how many pizzas to make available at the games. We have been provided with demand distributions for pizza based on past experience and know that Tom will only supply plain cheese and pepperoni and cheese combo pizzas. We also know that there is a fixed cost of $1,000 allocated equally between the two types of pizzas, and that the costs to make plain cheese pizza and pepperoni and cheese pizza are $4.50 and $5.00 respectively. Both pizzas sell for $9.00 and unsold pizzas have no value. The purpose of this report is to provide Tom with some information regarding how many of each type of pizza he should produce if he wants to achieve the highest expected profit from pizza sales at the game.

II. Analysis
In order to determine at which production level Tom will achieve the highest expected profit, it is first necessary to determine the potential profit or loss associated with producing at each demand level. To do this, a discrete probability distribution is composed for each potential level of production. For example, if 200 plain cheese pizzas are produced and 200 are demanded, the potential profit is $400. This profit consists of $1800 in sales revenue minus $1400 in costs ($900+$500 fixed). This profit will result regardless of whether more than 200 are demanded. Accordingly, if 400 cheese pizzas are produced and only 200 demanded, there is a potential loss of $500.

Using these distributions, we are then able calculate the distribution’s mean, which is the expected value of the profits at each level of production. The expected profits in this case are the weighted average of the potential profit values, in which the weights are the probabilities. The expected profits associated with each type of pizza are provided in the tables below:

...APStatistics Cole Rogers
Unit 7 Exam RandomVariables: Free Response
Directions: Complete the assignment on this paper. If you need additional paper make sure that you clearly label each page with your name. Your answers for this assignment must include reasons; simply stating the answer without justification will earn partial credit.
1. A Roulette wheel has 38 slots numbered 0 to 36 and 00. The wheel is spun and a ball is thrown into the wheel and comes to...

...SIDS31081 - Statistics Refresher
2006 – 2007
Exercises
(Probability and RandomVariables)
Exercise 1
Suppose that we have a sample space with five equally likely experimental outcomes :
E1,E2,E3,E4,E5.
Let
A = {E1,E2}
B = {E3,E4}
C = {E2,E3,E5}
a. Find P(A), P(B), P(C).
b. Find P(A U B) . Are A and B mutually exclusive?
c. Find Ac, Bc, P(Ac), P(Bc).
d. Find A U Bc and P(A U Bc)
e. Find P(B U C)
Exercise 2
A committee with two members is to be...

...selected at random from the sample.
a) What is the probability the person is female or occasionally involved in charity work?
b) Are the events “being female and occasionally involved in charity work” and “being frequently involved in charity work” mutually exclusive?
yes
6. A company gave psychological tests to perspective employees. The randomvariable x represents the possible test scores.
a) Use the histogram to find...

...be infected?
The probability that Alice’s RSA signature on a document is forged is () What is the probability that out of 4 messages sent by Alice to Bob at least one is not forged?
Event A is selecting a “red” card from a standard deck at random. Suggest another event (Event B) that is compatible with Event A.
What is the probability of getting 6 tails in 10 trials of tossing a coin? Solve this problem by using :The approximation mentioned in Theorem 6
The...

...THE MOMENTS OF A RANDOMVARIABLE
Definition: Let X be a rv with the range space Rx and let c be any known constant. Then the kth moment of X about the constant c is defined as
Mk (X) = E[ (X c)k ]. (12)
In the field of statistics only 2 values of c are of interest: c = 0 and c = . Moments about c = 0 are called origin moments and are denoted by k, i.e., k = E(Xk ), where c = 0 has been inserted...

...continuous randomvariable because the time is being measured. All possible results for the variable time (t) would be greater than > 0.
b) The weight of a T-bone steak is a continuous randomvariable because the weight of the steak is measured. All the possible results for the weight of the T-bone steak would be positive numbers making the variable weight (w) > greater than 0....

...that the attendant receives $7, $9, $11,
$13, $15, or $17 between 4:00 P. M. and 5:00 P. M. on any sunny Friday. Find the attendant’s expected earnings for this particular period.
4.7 By investing in a particular stock, a person can make a proﬁt in one year of $4000 with probability 0.3 or take a loss of $1000 with probability 0.7. What is this person’s expected gain?
4.10 Two tire-quality experts examine stacks of tires and assign a quality rating...

...Practice problem – V
Week 6
Four of the five sugars listed below are related as members of the same subgroup. Select the exception by indicating characteristic(s) of each option in the space provided thereby showing how the exception was determined. (3 marks)
a. glucose
b. fructose
c. cellulose
d. ribose
e. deoxyribose
Four of the five sugars listed below are related as members of the same subgroup. Select the exception by...