read the questions and answering

RMI 2101

Fall 2016

Homework Assignment 4

24 Points

Due on Monday, October 3, 2016 AT THE BEGINNING OF CLASS

Be careful to follow the Guidelines for Homework Document located in the Course

Documents Section of Blackboard. You will lose points for not following proper format.

This homework assignment has to be typed and submitted to Safe Assign.

1. The Temple football team is playing SMU on Saturday October 1, 2016. Suppose

that Temple has a 64.5% chance of winning the game. College football games

cannot end in a tie.

a. What is the random variable associated with this game? [1 point]

b. What is the mutually exclusive event in this case? [1 point]

c. Construct a well-labeled probability distribution table based on the

outcomes of this game. [2 points]

2. After SMU, Temple will play

Date GAME Win Probability1

October 1 SMU 64.5%

October 6 Memphis 24.0%

October 15 UCF 32.0%

October 21 South Florida 58.0%

October 29 Cincinnati 45.5%

November 4 Connecticut 69.0%

a. What is the probability that Temple wins ALL remaining games in the

regular season (all the ones listed in the above table)? [2 points]

b. Consider only the games in October. What is the probability that Temple

loses ONLY ONE of the October games? Be sure to show your work.

(Hint: they could lose against SMU AND win the others OR they could

lose against Memphis AND win the others…) [4 points]

3. On Thursday, ABC Grocery is expecting to receive one package [Package A]

containing $200 worth of food. Based on his past experience with the delivery

service, the manager estimates that this package has a chance of 20% being lost in

shipment.

On Friday, ABC Grocery expects another package [Package B] to be delivered.

Package B contains $300 worth of food. This package has a 25% chance of being

lost in shipment.

1 These win probabilities are randomly assigned.

a. What are the possible outcomes for ABC Grocery’s total dollar amount of

losses for package A and B? For each dollar amount of loss, describe

under what circumstances it would occur. In other words, what has to

happen in order for each dollar amount of losses to occur? Please note that

this asks about total dollar amount of losses, not number of losses.

[4 points]

b. For each of the possible outcomes you identify in part [a], derive the

probability of the outcome occurring. [2 points]

c. Construct [in table form] the probability distribution for total dollar

amount of losses for package A and B. [2 points]

d. Calculate the expected value of total dollar amount of losses. Round

your calculation to 4 decimal places. What are the units of measurement?

[2 points]

e. The manager has calculated the variance for the total dollar amount of

losses to be 23275. Since you want to be sure you are using correct

numbers in your evaluation, prove that the manager calculated the correct

variance for total dollar amount of losses. Show all work! Round each

calculation to 4 decimal places. What are the units of measurement?

[4 points]