Lisa, Jennie, and Rose run a 24-hour convenience store called PinkBlack, and each runs the store for equal non-overlapping 8-hour shifts. The number of customers that visit this store each day is random, and has a Poisson distribution with a mean of 6 customers per day. They also notice that, regardless of the time of day, the inter-arrival times between successive customers follow an exponential distribution. (a) What is the standard deviation of the inter-arrival time of customers, in hours? (b) Lisa sees a customer arrives at the store exactly halfway in her shift. What is the probability that no other customers will visit the store for the remainder of Lisa’s shift?
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!
Lisa, Jennie, and Rose run a 24-hour convenience store called PinkBlack, and each runs the store for equal non-overlapping 8-hour shifts. The number of customers that visit this store each day is random, and has a Poisson distribution with a mean of 6 customers per day.
They also notice that, regardless of the time of day, the inter-arrival times between successive customers follow an exponential distribution.
(a) What is the standard deviation of the inter-arrival time of customers, in hours?
(b) Lisa sees a customer arrives at the store exactly halfway in her shift. What is the probability that no other customers will visit the store for the remainder of Lisa’s shift?
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