The length of time for one individual to be served at a cafeteria is a random variable having an exponential distribution with a mean of 5 minutes. What is the probability that a) at least 50 of 100 randomly selected customers got served less than 4 minutes b) Out of 100 randomly selected customers, what is the probability that the average of their serving time is less than 6 minutes?
Added by Vanesa J.
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Using the exponential distribution formula, we have: P(X ≤ 4) = 1 - e^(-4/5) = 0.5507 Using the binomial approximation with n=100, we can calculate: P(X ≤ 49) = 100C49 * 0.5507^49 * (1-0.5507)^(100-49) = 0.1317 Therefore, the probability that at least 50 out of Show more…
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