In this video I go over another example on probability and average values and this time look at the probability of waiting longer than the average time we expect to wait when calling a company representative. What's interesting is that the average wait time does not necessarily mean that 50% of people wait at least this long. This is rather the median wait time and I will look at this further in my next video so stay tuned for that. The reason why the average wait time differs from the median wait time is because people with very long wait times skew the average value to be higher than when we base it strictly on finding the median value. This is a good example illustrating this concept so make sure to watch this video!
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Applications of Integrals: Probability: Average Values: Example 2
Suppose the average waiting time for a customer's call to be answered by a company representative is five minutes.
a) Find the probability that a call is answered during the first minute.
b) Find the probability that a customer waits more than five minutes to be answered.
Use the probability density function formula from Example 1:
Thus about 37% of customers wait more than mean waiting time of 5 minutes before their calls are answered.
If you were rather interested in the waiting time that would have 50% of people waiting more than and 50% waiting less than, this particular waiting time would be called the median wait time.
I will go over this further in the next video so stay tuned!