This time, Mr. Scapelli managed to eliminate the biases in the data through selecting the every 10th pizza delivery order and letting the customers inform their own pick-up times. The data is fine and appropriate for statistical use, and hence we can go through the statistical calculations.
Using Excel, we found the standard deviation and mean of the sample data for the total delivery time, preparation time, waiting time and travel time.
First, in order to discuss the viability of the company's 29-minute delivery guarantee strategy, we computed the following statistical parameters for the total delivery time.
MEAN(Total Time)STD(Total Time)
Then, the standardized Z value for P(Delivery Time>29) can be calculated as:
(29-25.9) / 4.08 = 0.76
P(Z>29) = 0.5 0.2764
The probability of delivery time being more than 29 minutes is higher than the targeted probability of 5 percent.
Further Recommendations for Improvement
In order to catch up the targeted probability of exceeding 29 minutes, there are two things that Mr. Scapelli can work on. First, he can take actions to decrease the expected time of the total delivery time. Alternatively, he can consider decreasing the variance of the delivery times. The breakdown of the total delivery time into preparation time, waiting time and travel time gives us some ideas for the improvement.
MEAN(Prep Time)STD(Prep Time)
Preparation of the pizzas takes 15.1 minutes on the average with a standard deviation of 1.1 minutes. The small standard deviation compared to the mean implies that the preparation process is pretty standard and variance of the preparation time is not very high. This is mostly due to the cooking requirements of the pizza. Maybe a new oven can be purchased for speeding up the cooking, however the oven capacity is sufficient at the moment.