# When 1500 orders are placed how many customers get a pizza for free in the following case: The amount of time it takes for a pizza to be delivered is normally distributed with a mean of 23.9 min, and standard deviation of 2.7 min. If anyone has to wait 30 min for an order, they get it for free.

The time taken to deliver a pizza is normally distributed with an average duration of 23.9 minutes and a standard deviation of 2.7 minutes. If a customer has to wait over 30 minutes for a pizza it is delivered for free. The number of people that get a free pizza...

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The time taken to deliver a pizza is normally distributed with an average duration of 23.9 minutes and a standard deviation of 2.7 minutes. If a customer has to wait over 30 minutes for a pizza it is delivered for free. The number of people that get a free pizza if 1500 orders are placed has to be determined.

First, find the z-score for 30. It is given by: (30 - 23.9)/2.7 = 2.259

From the normal table the value for 2.259 is 0.9878. The percentage of the area lying beyond 30 minutes is 0.0122

This gives the number of customers that get a free pizza as 1500*0.0122 = 18.3. Taking the higher integer gives 19.

Approximately 19 customers of the 1500 get a free pizza.