The amount of time a cashier spends cashing out each customer at a store is modeled by an exponential random variable with parameter λ = 1/3 minutes. Assume that the time the cashier spends with each customer is independent and identically distributed. Approximate the probability that the cashier will spend more than sixty minutes cashing out a total of eighteen customers. You may leave your solution as a real number rounded to four decimal places
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!
The amount of time a cashier spends cashing out each customer at a store is modeled by an exponential random variable with parameter λ =
1/3 minutes. Assume that the time the cashier spends with each customer is independent and identically distributed. Approximate the probability that the cashier will spend more than sixty minutes cashing out a total of eighteen customers. You may leave your solution as a real number rounded to four
decimal places or you may leave your solution in terms of the standard normal CDF, Φ.
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