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Many hospitals have implemented a triage process before accepting appointments in order to prioritize patients and minimize congestion. Consider a triage center with 7 staff members taking calls from customers. On average, one call arrives every 6 mins. Each staff member spends 20 mins with each customer on average (with a standard deviation of 15 mins). (a) What is the probability that one of their staff members is busy (as a %)? (b) What is the probability that a call can be immediately served? (c) How long (in minutes) does a customer spend on average waiting on hold before they can start speaking to a staff member? (d) How many customers on average are waiting to be served? (e) What is the probability that a customer spends more than 45 mins in the call center?

Many hospitals have implemented a triage process before accepting appointments in order to prioritize patients and minimize congestion. Consider a triage center with 7 staff members taking calls from customers. On average, one call arrives every 6 mins. Each staff member spends 20 mins with each customer on average (with a standard deviation of 15 mins). (a) What is the probability that one of their staff members is busy (as a %)? (b) What is the probability that a call can be immediately served? (c) How long (in minutes) does a customer spend on average waiting on hold before they can start speaking to a staff member? (d) How many customers on average are waiting to be served? (e) What is the probability that a customer spends more than 45 mins in the call center?

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.2: Expected Value And Variance Of Continuous Random Variables
Problem 10E
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Many hospitals have implemented a triage process before accepting appointments in order to prioritize patients and minimize congestion. Consider a triage center with 7 staff members taking calls from customers. On average, one call arrives every 6 mins. Each staff member spends 20 mins with each customer on average (with a standard deviation of 15 mins). (a) What is the probability that one of their staff members is busy (as a %)? (b) What is the probability that a call can be immediately served? (c) How long (in minutes) does a customer spend on average waiting on hold before they can start speaking to a staff member? (d) How many customers on average are waiting to be served? (e) What is the probability that a customer spends more than 45 mins in the call center?
Transcribed Image Text:Many hospitals have implemented a triage process before accepting appointments in order to prioritize patients and minimize congestion. Consider a triage center with 7 staff members taking calls from customers. On average, one call arrives every 6 mins. Each staff member spends 20 mins with each customer on average (with a standard deviation of 15 mins). (a) What is the probability that one of their staff members is busy (as a %)? (b) What is the probability that a call can be immediately served? (c) How long (in minutes) does a customer spend on average waiting on hold before they can start speaking to a staff member? (d) How many customers on average are waiting to be served? (e) What is the probability that a customer spends more than 45 mins in the call center?
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