Question

Read Questions Please. Its different from the others thats been posted!

Information

Six months before its annual convention, the American Medical Association (AMA) must determine how many rooms to reserve. At this time, the AMA can reserve rooms at a cost of $100 per room. The AMA believes the number of doctors attending the convention will be has a triangular distribution with minimum value 2000, maximum value 7000, and most likely value 5000. If the number of people attending the convention exceeds the number of rooms reserved, extra rooms must be reserved at a cost of $ 160 per room. Assume that there are 8000 rooms available.

[Round your answers to the nearest integer. Also just enter the number. For example, if your answer is $123,456, then enter 123456 without $ and comma.]

Information

Build a simulation model assuming the number of doctors attending the convention follows the following probability distribution.

Number	Probability
2500	0.05
3000	0.07
3500	0.09
4000	0.1
4500	0.12
5000	0.2
5500	0.15
6000	0.1
6500	0.06
7000	0.04
7500	0.02

Run the simulation model 50,000 times.

Question 4 (2 points)

The average number of doctors attending the convention is

Your Answer:

Question 5 (3 points)

The average number of extra rooms needed if they reserve 4000 rooms now is

Your Answer:

Question 6 (3 points)

If they reserve 4000 rooms now, the average number of extra rooms needed is

Your Answer:

Question 7 (3 points)

If they reserve 3000 rooms now, the expected total cost is

Your Answer:

Question 8 (3 points)

If they reserve 6000 rooms now, the expected total cost is

Your Answer:

Answer 1

Hello again, I'm glad you reposted the problem with other parts. I'd humbly suggest to post the entire problem in future, since the subparts are mostly correlated, hence the solution can be easily provided in one go.

One more thing, in my last solution I inadvertently interchanged the "Actual" and "Expected" labelling, which has led to the expected total cost being based on the triangular distribution, instead of the Discrete distribution that has been provided. Pardon me for the same, here I am providing the same solution again with correction. All the formulas are still structured the same, just need to use the correct distribution

Question 4 This is a pretty striaghtforward calculation, obtained using the formula

Actual Attendee Probability Distribution
Number	Probability	CDF	Percentage	Number	Avg. Doctors
2500	0.05	0	0%	2500	125
3000	0.07	0.05	5%	3000	210
3500	0.09	0.12	12%	3500	315
4000	0.1	0.21	21%	4000	400
4500	0.12	0.31	31%	4500	540
5000	0.2	0.43	43%	5000	1000
5500	0.15	0.63	63%	5500	825
6000	0.1	0.78	78%	6000	600
6500	0.06	0.88	88%	6500	390
7000	0.04	0.94	94%	7000	280
7500	0.02	0.98	98%	7500	150
					4835

Here I am also sharing a snapshot of the average value obtained from the 50,000 simulations, which can be seen at bottom right and is brutally close to the theoretical value. You can also see the amends I've made here.

Question 5, 6 Seems to be some misprint there? Both problems are asking the same thing, perhaps a different number should have been there

Again this is a straightforward computation, done using the formula

Actual Attendee Probability Distribution
Number	Probability	Extra Room (4000 Booked)	Expected Extra Room Calculation
2500	0.05	0	0
3000	0.07	0	0
3500	0.09	0	0
4000	0.1	0	0
4500	0.12	500	60
5000	0.2	1000	200
5500	0.15	1500	225
6000	0.1	2000	200
6500	0.06	2500	150
7000	0.04	3000	120
7500	0.02	3500	70
			1025

Question 7, 8 Corrections are as under

Based on the excel snapshot shown above, the formulas are

Actual : =VLOOKUP(RAND(),$D$3:$E$13,2,TRUE)

Expected : =VLOOKUP(RAND(),$D$20:$E$5020,2,TRUE)

Actual < 3000? : =IF(G2<=3000,1,0)

Cost : =IF(I2=1,G2*100,300000+160*(G2-3000))

The value hovers mostly from about 594000 to 596000. I'd say the best value to report would be 595000.

For Actual < 6000, we obtain

The value hovers mostly from about 488000 to 491000. Best value to report would be 489500