Final answer:
To calculate the actual inter-arrival times, subtract the arrival time of one customer from the previous one, and the mean arrival rate of customers per hour is the total number of customers divided by the total time in hours. Exponential and uniform distributions are used for modeling different waiting time scenarios.
Step-by-step explanation:
To calculate the actual customer inter-arrival times using the Pancho's Burritos spreadsheet, you would subtract each customer's arrival time from the previous customer's arrival time. The mean arrival rate of customers per hour is found by dividing the total number of customers by the total observation time in hours.
Referring to the information provided: if an average of 30 customers arrives per hour, it translates to one customer every two minutes, given that there are 60 minutes in an hour. For part b, if one customer arrives every two minutes, then logically it would take six minutes for three customers to arrive.
For the exponential distribution examples, the probability questions such as in part c and d can be answered using the exponential probability density function. However, without the actual arrival times data, we cannot specifically calculate these probabilities.
In the case of the uniform distribution mentioned for the rural bus wait times and the Sky Train wait times, the mean time between arrivals can be calculated as half of the maximum waiting time. For example, if the maximum waiting time is 75 minutes, the average would be 37.5 minutes between arrivals. To find when 70% of customers arrive, you use the 70th percentile of the relevant probability distribution function.