Customers are serviced at a rate of three customers per hour according to an exponential distribution.What is the probability that customer service will require fewer than 10 minutes?
A)less than or equal to 0.40
B)greater than 0.40 but less than or equal to 0.45
C)greater than 0.45 but less than or equal to 0.50
D)greater than 0.50

Question

Quizplus · Accepted Answer

We first need to convert the service rate from customers per hour to customers per minute. 
Three customers per hour = 3/60 = 1/20 customers per minute.

Next, we need to find the probability that customer service will require fewer than 10 minutes.

Using the exponential distribution formula: 
P(X < 10) = 1 - e^(-λx) 
where λ is the service rate (1/20) and x is the time in minutes (10).

P(X < 10) = 1 - e^(-1/20 * 10) 
P(X < 10) = 1 - e^(-1/2)

Calculating this out, we get: 
P(X < 10) ≈ 0.393

So the answer is A, less than or equal to 0.40.

Customers Are Serviced at a Rate of Three Customers Per