At a train station, there are 7 ticket vending machines. Customers form a single waiting line to buy tickets from one of the machines. It is observed that the interarrival time is exponentially distributed with its mean equal to 1.6 minutes. On average, it takes a customer 7 minutes to buy a ticket, with a standard deviation of the time estimated as 4 minutes. On average, how many customers are waiting in the line?

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.6: Exponential And Logarithmic Equations
Problem 69E
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please answer in 30 minutes.
At a train station, there are 7 ticket vending
machines. Customers form a single waiting line to
buy tickets from one of the machines. It is observed.
that the interarrival time is exponentially distributed
with its mean equal to 1.6 minutes. On average, it
takes a customer 7 minutes to buy a ticket, with a
standard deviation of the time estimated as 4
minutes.
On average, how many customers are waiting in the
line?
Transcribed Image Text:At a train station, there are 7 ticket vending machines. Customers form a single waiting line to buy tickets from one of the machines. It is observed. that the interarrival time is exponentially distributed with its mean equal to 1.6 minutes. On average, it takes a customer 7 minutes to buy a ticket, with a standard deviation of the time estimated as 4 minutes. On average, how many customers are waiting in the line?
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