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Sagot :
The answer of this question is found to be 0.0012.
The mean total service time is 10 minutes times lambda (the average number to turn up during the hour)
Lambda is 7, since the average rate is 7 per hour and your time window is 1 hour.
mean service time = 7 × 10 = 70 minutes.
For a poisson process, lambda is both the mean and variance of the arrivals.
So the variance = 10² × lambda = 700, since we want the variance of the service time, rather than the variance of the arrival rate.
This is because:
σ(aX) = a × σ(X).
and σ = sqrt(variance)
σ(service time) = 10 σ(arrival time)
variance(service time) = (10 × σ(arrival time))²
variance(service time) = 100 × variance(arrival time) = 100 × lambda = 100 × 7
mean(servicetime) = 70
variance(servicetime) = 700
2.5 hour = 150 min
Z = [tex]\frac{(S - 70)}{\sqrt{700} }[/tex] follow N(0,1)
P(S > 150) = P( [tex]\frac{(S - 70)}{\sqrt{700} }[/tex]> [tex]\frac{(150 - 70)}{\sqrt{700} }[/tex])
=P(Z > -2.5512)
=0.0012
Learn more about probability here ;
https://brainly.com/question/13604758
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