Question

At a certain bank, the amount of time (in minutes) that a customer spends being served by a teller is an exponential random variable with mean 5 minutes. (a) What is the probability that a customer will spend at least 6 minutes with a teller? (b) If there is a customer who has been in service for 2 minutes when you enter the bank, what is the probability that he or she will still be with the teller after an additional 5 minutes?

          At a certain bank, the amount of time (in minutes) that a customer spends being served by
a teller is an exponential random variable with mean 5 minutes.
(a) What is the probability that a customer will spend at least 6 minutes with a teller?
(b) If there is a customer who has been in service for 2 minutes when you enter the bank, what is
the probability that he or she will still be with the teller after an additional 5 minutes?

At a certain bank, the amount of time (in minutes) that a customer spends being served by
a teller is an exponential random variable with mean 5 minutes.
(a) What is the probability that a customer will spend at least 6 minutes with a teller?
(b) If there is a customer who has been in service for 2 minutes when you enter the bank, what is
the probability that he or she will still be with the teller after an additional 5 minutes?

Added by Shawn M.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Sri K

11/08/2022

Step 1

In this case, the mean is 5 minutes, so λ = 1/5 = 0.2. The probability that a customer will spend at least 6 minutes with a teller is given by the integral from 6 to infinity of the probability density function, which is equal to e^(-λx). So, the probability is Show more…

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Problem 4 At a certain bank, the amount of time (in minutes) that a customer spends being served by a teller is an exponential random variable with mean 5 minutes. (a) What is the probability that a customer will spend at least 6 minutes with a teller? (b) If there is a customer who has been in service for 2 minutes when you enter the bank, what is the probability that he or she will still be with the teller after an additional 5 minutes?