A new local game store just opened in your neighborhood! For the owner, Edna Davis, this had been her childhood dream. She has always loved playing board games with her friends, and now she has decided to take a step forward and make a living out of her passion! The new store will mainly sell board games and trading card games (TCGs).

Thinking long term, Edna believes that in her first year of running the business, she should put her focus on building a strong community of TCG players that go to the store to play. Most likely, these players will become recurrent customers of the store and buy multiple products. She will start selling one TCG product: BlueWizard.

It took Edna almost 10 years to save enough money to open this business, as she needed enough cash to decorate the store, pay bills, and buy initial inventory positions. Now, Edna needs your help with analyzing how much product she should buy for each item in order to optimize her cash allocation.

One of BlueWizard's most popular products is Universe GL16.

1. Considering that monthly sales of Universe GL16 can be modeled as a Normal Distribution with a mean of 525 boxes and a standard deviation of 131 boxes, what's the probability of selling 600 boxes or less of this product in a given month?

2. If Edna orders 700 boxes of Universe GL16, what's the probability of stocking out (meaning that the demand exceeds the number of boxes in stock) in a given month?

Store attendance is another big concern for Edna, as she does not want to have customers shopping unattended for too long. Considering that customers arrivals per hour can be modeled as Poisson Distribution with a =4.7:

3. What's the probability of having more than 5 people arriving at the store in one hour?

4. What's the probability of having exactly 3 people arriving at the store in one hour?

BlueWizard can be played in-person by two or more players, so Edna decided to run weekly events where players can play against each other in the store. However, it has been difficult for her to estimate how many players will attend those events.

After the first 4 months, the event attendance historical data is still limited. Edna thinks that the triangle distribution can be a good start to model the number of attendees in future events. Considering the data in Table 1:

Event#	Number of Attendees
1	14
2	26
3	66
4	87
5	66
6	66
7	41
8	64
9	37
10	66
11	55
12	66
13	78
14	66
15	34

What would be the a parameter for this distribution?

What would be the b parameter for this distribution?

What would be the c parameter for this distribution?

If Edna has 75 seats ready for these events, what is the probability that some of the attendees do not get a seat at one of these events?

Finally, BlueWizard has sent some promo cards and other supplemental products free of charge to Edna so she can distribute them among players at each event, which will help build a stronger community. Next week there is a new event, and there is a limited number of gifts that will be given to players, which can be classified in 4 categories:

Promo Card	Deck Box	Binder	Playmat
15	15	16	14

Considering that these limited gifts will be randomly picked for each player that arrives at the event, and that only the first 60 players can get a gift (one gift per player), Edna wants to know the following:

What is the probability that the first player receives a Binder?

What is the probability that the first two players will both receive a Binder?

If the first two players have already received a Binder, what is the probability that the third player gets a Deck Box?