A coffee shop makes and dispenses hot beverages and orders a

A coffee shop makes and dispenses hot beverages and orders arrive according to a Poisson process at a rate of 10 per hour. After placing an order, the customer immediately gets his or her drink, and the temperature of each drink is uniformly distributed between 120 and 140 degrees. However, a customer is only satisfied if the temperature of the drink is at least 130 degrees.

For each of the following random variables, specify the name and parameter(s) of its distribution.

(a) The time until the first order of the day is placed.

(b) The number of orders placed until a satisfied customer gets a drink.

(c) The number of the first ten customers of they day that are satisfied with their orders.

(d) The number of orders made between 8 am and 12 pm.

(e) The number of orders placed between 12 pm and 1 pm, given that 36 orders were placed between 8 am and 12 pm.

(f) The number of orders placed between 11 am and 12 pm, given that 36 orders were placed between 8 am and 12 pm.

Solution