Exam 10: Simulation Modeling

Suppose that IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. a.Suppose that 1000 individuals took the IQ examination.Use Crystal Ball to simulate their scores. b.What is the mean of the simulated IQ scores? c.Suppose that being in the top 2% qualifies an individual as a genius.Using the simulated IQ scores,what should the IQ score be to qualify as a genius?

John Smith is planning to refinance his home mortgage to take advantage of the lower current interest rates.As part of the refinancing application,the bank needs to appraise Mr.Smith's home.Mr.Smith expects an appraisal of at least $175,000 but no more than $250,000.All values between $175,000 and $250,000 have the same probability of being the actual appraised value.What is the appropriate distribution for simulating appraisal values?

You have just graduated with an MBA degree and accepted your first job at the age of 25.You are thinking ahead for early retirement and you plan on saving $5000 at the end of each year.You expect each year's return to be modeled as a normal distribution with a mean of 10% and standard deviation of 2.5%.Suppose you intend to retire at the age of 55.Use Crystal Ball to simulate the ending investment value.Use 1000 replications. a.What is the average amount of money that you will have at retirement? b.What is the probability of having more than $1,000,000 at retirement?

Consider a single deck of cards.Use Crystal Ball to determine the odds of drawing 2 aces without replacement.Use 1000 replications.

Consider the event of tossing three coins.You are interested in computing the probability of getting three heads.Use Crystal Ball to simulate the event of tossing three coins 1000 times. a.What is the theoretical probability of getting three heads? b.What is the percentage of getting three heads using the 1000 simulated values?

Excel uses the RAND()function to generate discrete values between 0 and 1.

Use this information and output to answer the following questions. Rentals-R-Us specializes in 4WD car rentals.The number of rentals per month typically ranges between 10 and 50.You may assume equal probability for the number of rentals to assume any value in that range.The monthly operating costs for Rentals-R-Us can range anywhere from $2,000 to $4,000,with $3,000 being the most probable cost.Each rented vehicle generates $55 in revenues.You decide to build a simulation model in Crystal Ball to simulate monthly profits. A B 1 Rentals-R-Us 2 Number of car rentals 50 3 Rental per car \ 55 4 Monthly operating costs \ 2,000 5 Profit or loss \ 750 -Refer to the table.What is the appropriate distribution for the variable "Monthly operating costs"?

Which of the following is considered a disadvantage of simulation?

For the daily lottery in a given state,participants select three numbers between 0 and 9.You feel lucky and buy 1000 tickets from a 7-Eleven store.Suppose that the winning number is 999.Using Crystal Ball,simulate the outcomes of 1000 tickets to compute the odds of winning the lottery.Note that it is possible for 2 or more of your tickets to have the winning numbers.

Use this information to answer the following questions. The manager of an opera theater is concerned about overbooking one of his upcoming concerts.The theater has 300 seats,but sometimes there are empty seats.Tickets cost $50 per seat.Historical records demonstrate that about 9% of reservation holders do not show up.If the manager overbooks and more than 300 individuals show up,some of them will be given guaranteed reservations and VIP seats to the next coming show.Moreover,to keep his customers happy,the manager gives each individual who is bumped $20 worth of gift certificates. -Refer to the information above.Suppose that the manager wishes to examine the effect of different reservation levels on the average weekly total costs.In specific,the manager wishes to consider levels of 290,300,310,and 320.Use Crystal Ball's Decision Table to find the reservation level that maximizes average profit.Use 1000 replications.

Simulation usually generates optimal solutions.

A Decision Table is used in Excel to try at most 2 values automatically for a parameter in the model.

Consider the following game involving a single die.Someone offers to give you $1 if you toss a 1,$2 if you toss a 2,$3 if you toss a 3,etc.In other words,your earnings will correspond to the face value of the die.However,to play this game,each toss will cost you $2.50.You decide to use Crystal Ball to simulate your net earnings per toss based on 1000 simulation runs.What is your mean net earning per toss based on the simulated sample values?

Consider the following PERT network,along with the completion times for each activity,in days.Use Crystal Ball to enumerate the completion times of all paths in the network.Typically,the longest path in the network dictates the project completion time.Use 1000 replications. Activity Optimistic Pessimistic 1-2 3 5 7 2-4 15 20 30 4-6 16 18 21 1-3 4 5 6 3-5 10 15 19 5-6 16 20 25 a.What is the average project completion time? b.What is the probability that the project completion time will exceed 50 days?

The sum of all previous probabilities up to the current probability is the ________.

Use this information to answer the following questions. The manager of an opera theater is concerned about overbooking one of his upcoming concerts.The theater has 300 seats,but sometimes there are empty seats.Tickets cost $50 per seat.Historical records demonstrate that about 9% of reservation holders do not show up.If the manager overbooks and more than 300 individuals show up,some of them will be given guaranteed reservations and VIP seats to the next coming show.Moreover,to keep his customers happy,the manager gives each individual who is bumped $20 worth of gift certificates. -Refer to the information above.The manager wishes to explore the impact on profitability if 310 reservations are accepted.Use Crystal Ball with 1000 replications.

Daily demand for bananas at a grocery store is normally distributed with a mean of 100 lbs and standard deviation of 20.Use Excel to set up a Monte Carlo simulation of 12 months.

Use this information to answer the following questions. The Gambler Hotel in Las Vegas has 300 rooms that each rent for $175 per night.For each reservation accepted,there is a 7% chance that the guest will not arrive.If the hotel overbooks,it incurs $220 for each reservation that is not honored. -Refer to the information above.Suppose that the manager wishes to examine the effect of different reservation levels on average profitability.In specific,the manager wishes to consider reservation levels of 280,290,300,310,and 320.Use Crystal Ball's Decision Table to find the reservation level that maximizes average profitability.Use 1000 replications.

The Excel function =RAND()generates random numbers that are:

A five-star hotel accepts 100 room reservations daily.For each reservation accepted,there is a 7% chance that the guest will not arrive.You decide to build a simulation model to describe the number of guests who will show up.The best appropriate distribution to use is: