**Question 14**Cece serves customers who arrive at The Griffin, and arrivals in an hour are known to follow a Poisson distribution. The probability that no customers arrive in an hour is 0.0005. What is the average number of customers that arrive at The Griffin in an hour?---**Explanation:**This question involves using the Poisson distribution to determine the average rate (λ) at which customers arrive at The Griffin. The Poisson distribution is given by:\[ P(X = k) = \frac{e^{-\lambda} \lambda^k}{k!} \]where \( P(X = k) \) is the probability of \( k \) events (customer arrivals) in a fixed interval and \( e \) is the base of the natural logarithm.Here, \( k = 0 \), and \( P(X = 0) = 0.0005 \).Thus:\[ 0.0005 = \frac{e^{-\lambda} \lambda^0}{0!} \]\[ 0.0005 = e^{-\lambda} \]To find λ, solve the equation:\[ \lambda = -\ln(0.0005) \] Calculating this will give the average number of customers that arrive at The Griffin in an hour.

Cece serves customers who arrive at The Griffin, and arrivals in an hour are known to follow a Poisson distribution. The probability that no customers arrive in an hour is 0.0005. What is the average number of customers that arrive to The Griffin in an hour?

Cece serves customers who arrive at The Griffin, and arrivals in an hour are known to follow a Poisson distribution. The probability that no customers arrive in an hour is 0.0005. What is the average number of customers that arrive to The Griffin in an hour?

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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