Service time in a coffee shop follows exponential distribution with an average service time of 6 minutes. Probability that a service takes more than 6 minutes is equal to
A) 0.500
B) 0.368
C) 0.632
D) 0.263

Question

Quizplus · Accepted Answer

The exponential distribution is given by the formula $P(X > x) = e^{-\lambda x}$, where $\lambda = \frac{1}{\text{mean}}$. Given the mean service time is 6 minutes, $\lambda = \frac{1}{6}$. For $P(X > 6)$, we substitute $x = 6$ into the formula, resulting in $P(X > 6) = e^{-6/6} = e^{-1} \approx 0.368$.

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