Service time in a coffee shop follows exponential distribution with an average service time of 6 minutes. Probability that a service takes between 4 and 8 minutes is equal to
A) 0.248
B) 0.513
C) 0.736
D) 0.263

Question

Quizplus · Accepted Answer

The probability density function of an exponential distribution is given by:```f(x) = (1/λ) * e^(-x/λ)```where λ is the average service time.In this case, λ = 6 minutes.The probability that a service takes between 4 and 8 minutes is given by:```P(4 < X < 8) = ∫[4,8] (1/6) * e^(-x/6) dx``````= -e^(-x/6) |[4,8]``````= -e^(-8/6) + e^(-4/6)``````= 0.248```Therefore, the correct answer is A) 0.248.

Service Time in a Coffee Shop Follows Exponential Distribution with an Average