Question 2 [18 marks] The average time between customers at Papyrus Café is 3 minutes. Customer arrivals occur randomly and independently of one another, and a customer just arrived. Each customer spends between a minimum of $3 and a maximum of $25 with each amount in between being equally likely. On average throughout the day, 1 out of 4 customers have to order their second preference item(s), because Papyrus is out of stock of their first preference. The customer spend remains the same regardless of whether they purchased their first or second preference. a) What is the standard deviation of the time between customers? [2 marks] [2 marks] [2 marks] b) What is the probability that exactly one customer arrives in the next 300 seconds? [2 marks] c) What is the probability that the next customer arrives in the next minute? d) What is the probability that the next customer arrives in 2 to 4 minutes time? e) What is the probability that the next customer spends more than $10 dollars? [2 marks] f) What is the probability that 22 customers arrive in the next hour and at least 80% of them receive their first preference item? [4 marks] g) If 31 customers arrive in the next hour, what is the probability that they spend less than $12 on average? [4 marks]