If the mean waiting time for the next arrival is 18 minutes, what is the first quartile (25^th percentile) for waiting times? A)13 minutes B)7.9 minutes C)5.2 minutes D)3.1 minutes

Question

Quizplus · Accepted Answer

The first quartile (25th percentile) represents the point at which 25% of the waiting times fall below it. We can use the exponential distribution formula to find the value of the first quartile: 
Q1 = -ln(1-0.25)/λ 
where λ is the rate parameter of the exponential distribution (the reciprocal of the mean waiting time). 
Plugging in λ = 1/18, we get: 
Q1 = -ln(0.75)/ (1/18) ≈ 5.2 minutes 
Therefore, the correct answer is C.

If the Mean Waiting Time for the Next Arrival Is