1. ACME Construction is taking on two projects in 2022. The first project is an office building
   in downtown Philadelphia. If they do not finish the project on time there are penalties. They
   have a 80% probability of finishing on time – which results in no penalty. They have a 20%
   chance of being late which will result in a $1,000 penalty. The second project is a new dorm
   on the Temple campus. If they do not finish the project on time there are penalties. They have
   a 40% chance of finishing on time – which results in no penalty. They have a 60% chance of
   being late which will result in a $6,000 penalty.
   a. What is the probability that both projects will be completed on time? (1 point)
   b. What is the probability that both projects will be late? (1 point)
   c. What is the expect cost (penalty) of the projects that ACME is doing for 2022? (2 points)
2. As the risk manager for the Philadelphia airport you want to collect data on specific airline delays
   and how it could impact the airports revenue. You start by looking into American Airlines and
   how many delays they have per day due to repairs. American Airlines has 40 airplanes operating
   out of Philadelphia airport. Below is the data you have collected.

of delays per day per plane Probability

0 0.10
1 0.15
2 0.26
3 0.32
4 0.13
5 0.04
a. Calculate the expected frequency of delays per day. (2 points)
b. Calculated the variance. (2 points)
2

3. Now assume that when delays do occur, they are random and losses due to cost repairs and time
   delays breakdown as follows – 50% of the time they cost $2,000, 30% of the time they cost
   $3,500 and 20% of the time they cost $6,000
   a. Calculate the expected cost per delay? (2 points)
   b. Calculate the expected losses for ALL planes per day. (2 points)
   c. Calculate the expected losses for ALL planes for the whole year. (1 point)
4. You then collect data on Jet Blue who operates 25 airplanes out of Philadelphia airport. Below is
   the data you have collected on delays per plane per day.

of delays per plane per day # of planes having these losses

0 4
1 6
2 ??
3 5
4 1
a. Calculate the probability distribution for frequency based on the information provided
above. (2 points)
b. Which airline faces the most risk for delays between American Airlines and Jet Blue?
Show/explain how you came to this answer. (3 points)

5. From past information, you collect the following data related to dollar amount of losses per plane
   per day when delays to do occur for Jet Blue.
   $ amount of losses Probability of dollar loss
   1,500 0.15
   2,000 0.30
   3,000 0.45
   5,000 0.10
   a. Calculate the expected value of severity for Jet Blue. (2 points).
   b. Calculate the expected loss per plane per day. (1 point)
6. Jackie, a passionate EMT, works every Sunday. This day of the week tends to be the busiest with
   the amount of calls they get. Jackie is required to document the amount of calls she goes on every
   shift. Below is the data she has collected for the past year (52 weeks).

of calls # of Sundays

0 3
1 10
2 16
3 ????
4 8
a. Create a probability distribution. (2 points)
3
b. Calculate the coefficient of variation. (2 points)

7. Two students are enrolled in RMI 2101. Jerry has a 3.5 GPA and Shanan has a 2.0 GPA. Jerry
   has a variance of 0.6 and Shanan has a variance of 0.5 – mathematically prove and identify who
   faces the most risk. You must show the calculation for each student to receive any points. (3
   points)