Suppose that the customers are standing in a line to be served by a teller in a bank. The amount of time each customer spends with the teller is exponentially distributed with mean 10 minutes. (a) What is the probability that a customer will spend more than 15 minutes with the teller? (b) What is the probability that a customer will spend more than 15 minutes with the teller given that he is still in the bank with the teller after 10 minutes?
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!
. Suppose that the customers are standing in a line to be served by a teller in a bank. The amount of time each customer spends with the teller is exponentially distributed with mean 10 minutes.
(a) What is the probability that a customer will spend more than 15 minutes with the teller?
(b) What is the probability that a customer will spend more than 15 minutes with the teller given that he is still in the bank with the teller after 10 minutes?
(c) Suppose the teller starts to serve the first customer at 2:00pm. What is the probability that the teller FINISHES serving at least 2 people between 2:00pm to 2:30pm?
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