A family-run inn has 76 rooms. The inn is considering the use of overbooking, because the frequency of no-shows has left many rooms vacant during the past summer season. Based on the past experience, the number of no-shows is an approximated normal distribution with a mean of 11 and a standard deviation of 2. Assume the cost of over-estimation is $15 and the cost of under-estimation is $30. Use the assumed cost values to find the maximum number of reservations that the inn should take every day. Note that normsinv(0.3333) = -0.4, normsinv(0.6667) = 0.4
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
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