Central Limit Theorem — A Real Life Case Study
Hello everyone,
Today, I am going to solve a real life business challenge using Central Limit Theorem (CLT). If you want to know about CLT, you can find it here,
A business client of FedEx wants to deliver urgently a large freight from Denver to Salt Lake City. When asked about the weight of the cargo they could not supply the exact weight, however they have specified that there are total of 36 boxes.
You are working as a Business analyst for FedEx. And you have been challenged to tell the executives quickly whether or not they can do certain delivery.
Since, we have worked with them for so many years and have seen so many freights from them we can confidently say that the type of cargo they follow is a distribution with a mean of μ= 72 lb (32.66 kg) and a standard deviation of σ = 3 lb (1.36 kg).
The plane you have can carry the max cargo weight upto 2640 lb (1193 kg).
Based on this information what is the probability that all of the cargo can be safely loaded onto the planes and transported?
The approach:
Steps:
- Using CLT, find the mean and std deviation of the sample mean.
- Next, calculate the critical mass (X crit) of each box by dividing the allowable capacity of the plane to carry weight with the total number of boxes. So, to safely takeoff the plane, the average weight of the each box should not exceed 73.06 lb/box.
- Finally, calculate the Z-score from the above formula and then we refer the Z value from the table here to find out the probability.
Now, you can go to the manager and tell him that I have done the calculations and the probability that the plan can safely takeoff is 98.3% and 1.7 % chance it cannot takeoff.
And now its up-to the manager to make a decision whether they are ready to take risk of 1.7% or not.
Hope you enjoyed it and I will be back with more new contents!!!
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