The distribution of durations for which apartments remain empty after the resident moves out for one property management company over the past 10 years was approximately normal with mean u = 85 days and standard deviation o = 29 days. The property management company tags the files of the apartments that were empty for the shortest 5% of durations to have priority cleaning the next time their residents move out. What is the maximum duration for which an apartment remained empty for the company to tag its file? Round to the nearest whole number.
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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