Pronto Pizza Revisited
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.
Statistical Efforts
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)
25.90 4.08087296
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
= 0.2236
= %22
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)
15.11 1.105976378
Preparation of the pizzas takes 15.1 minutes on the average with a standard devia ...