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Question 9 The time between emergency calls to a fire station averages 2 hours and follows an exponential distribution. Phil, the fireman, has just started his 8:00 am shift. (a) What is the probability that the next emergency call comes in after 11 am? (b) Phil has nearly finished his shift: 30 minutes to go. There has been no call during his shift so far. What is the chance of a call in the next 30 minutes? P(at most or less than) = $1 - e^{-\lambda x}$ P(at least or more than) = $e^{-\lambda x}$ $\lambda = \frac{1}{\text{Mean time}} = $ average number of events per time unit

          Question 9
The time between emergency calls to a fire station averages 2 hours and follows an
exponential distribution. Phil, the fireman, has just started his 8:00 am shift.
(a) What is the probability that the next emergency call comes in after 11 am?
(b) Phil has nearly finished his shift: 30 minutes to go. There has been no call during
his shift so far. What is the chance of a call in the next 30 minutes?
P(at most or less than) = $1 - e^{-\lambda x}$
P(at least or more than) = $e^{-\lambda x}$
$\lambda = \frac{1}{\text{Mean time}} = $ average number of events per time unit

Question 9
The time between emergency calls to a fire station averages 2 hours and follows an
exponential distribution. Phil, the fireman, has just started his 8:00 am shift.
(a) What is the probability that the next emergency call comes in after 11 am?
(b) Phil has nearly finished his shift: 30 minutes to go. There has been no call during
his shift so far. What is the chance of a call in the next 30 minutes?
P(at most or less than) = 1 - e^-λ x
P(at least or more than) = e^-λ x
λ = (1)/(Mean time) = average number of events per time unit

Added by Julie W.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Aarti Kumari

12/16/2021

Step 1

Since the average time between emergency calls is 2 hours, we can calculate the average number of emergency calls per hour by taking the reciprocal of the average time between calls: Average number of emergency calls per hour = 1 / 2 = 0.5 Show more…

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The time between emergency calls to a fire station averages 2 hours and follows an exponential distribution. Phil, the fireman, has just started his 8:00 am shift. a) What is the probability that the next emergency call comes in after 11:00 am? b) Phil has nearly finished his shift with 30 minutes to go. There has been no call during his shift so far. What is the chance of a call in the next 30 minutes? P(at most or less than) = 1 - e^(-x) = average number of events per time unit (Mean time)