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Question 2

You are operating a Fried Chicken restaurant named "Chapman's Second Best Chicken and Waffles"

In a given night you are open to customers from 5pm to 9pm

When you are open, customers arrive at an average rate of 5 people every 30 minutes. Individuals are equally likely to arrive at any point in time, andprevious arrivals do not impact the probability of additional arrivals. You can handle a maximum of 100 customers a night.

On any given night, the amount that guests on average spend at your restaurant is uniformly distributed between $10 and $30(to be clear, it is the overall average level of spending per guest which is uniformly distributed, not the spending of each individual guest)

The distribution of spending per-person is statistically independent of the number of guests that arrive on a given night.

2.1For every customer you need to purchase 4 chickens. What is the minimum amount of chickens should you purchase to be 95% confident you will have enough food for a night?(note, you can only purchase a whole number of chickens)

2.2If you have 10 chickens, what is the probability that you will run out of food by the end of the night?

2.3aWhat is the expected amount of revenue per guest on a given night?

2.3bWhat is the expected TOTAL amount of revenue from guests on a given night?Your costs for keeping the restaurant open on a night are $500.

2.4aSuppose that you expect 25 customers to arrive. What is the conditional probability that you will collect more than $500 total revenue?

2.4bWhat is the probability of exactly 25 customers arriving?

2.4cWhat is the joint probability of exactly 25 customers arriving AND collecting more than $500 in total revenue

2.4What is the percent chance that you will receive at least $500 in total revenue?Hint: Note that if 50 or more customers arrive you are certain to raise more than $500 in revenue, and if less than 17 arrive you are certain to fail