Answer:
(a) 0.2885
(b) 0.0736
(c) 0.0468
Step-by-step explanation:
The exponential distribution of Wendy's service time is given by:
P(x) = [exp (-x/μ)]/μ............................................................................ (1)
P(x) = Probability function
x = Service time, in minute
μ = average service team, in minute, 2.2 minutes
(a) x= 1, substituting into equation (1) we have:
P(1) = [exp (-1/2.2)]/2.2
= 0.6347/2.2
= 0.2885
(b) x₁ = 0.5 minutes
x₂ = 1 minute
P (0.5<x<1) = P(0.5) -P(1) ----------------------------------------------- (2)
From (a), P (1) = 0.2885
P(0.5) =P(1) = [exp (-0.5/2.2)]/2.2
= 0.7967/2.2
= 0.3621
Substituting into (2), we have :
P (0.5<x<1) = 0.3621 -0.2885
= 0.0736
(c) P(5) = [exp (-5/2.2)]/2.2
= 0.1030/2.2
= 0.0468
