Customers arrive to check in at the exclusive and expensive Regency Hotel’s lobby at a rate of 40 per hour (Poisson distributed). The hotel normally has three clerks available at the desk to check in guests. The average time for a clerk to check in a guest is 4 minutes (exponentially distributed). Clerks at the Regency are paid $24 per hour, and the hotel assigns a goodwill cost of $2 per minute for the time a guest must wait in line. Determine whether the present check-in system is cost-effective. If it is not, recommend what hotel management should do.
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!
Customers arrive to check in at the exclusive and expensive Regency Hotel’s lobby at a rate of
40 per hour (Poisson distributed). The hotel normally has three clerks available at the desk to
check in guests. The average time for a clerk to check in a guest is 4 minutes (exponentially distributed).
Clerks at the Regency are paid $24 per hour, and the hotel assigns a goodwill cost of
$2 per minute for the time a guest must wait in line. Determine whether the present check-in
system is cost-effective. If it is not, recommend what hotel management should do.
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