Solve the problem.
-The time (in minutes) a customer must wait in line at a bank is a continuous random variable with probability density function f(x) as shown below. Find the median waiting time. Round to three decimal places.
A) 0.693 minutes
B) 0.143 minutes
C) 3.892 minutes
D) 4.852 minutes

Question

Solve the problem.
-The time (in minutes) a customer must wait in line at a bank is a continuous random variable with probability density function f(x) as shown below.  Find the median waiting time. Round to three decimal places.
A) 0.693 minutes 
B) 0.143 minutes 
C) 3.892 minutes 
D) 4.852 minutes

Quizplus · Accepted Answer

To find the median waiting time, we need to find the value of x that satisfies:

∫0x f(t) dt = 0.5

Using the given probability density function, we have:

∫0x (1/6)*t^2 dt = 0.5

Integrating gives:

(1/18)*x^3 = 0.5

x^3 = 9

x ≈ 2.08

Therefore, the median waiting time is approximately 2.08 minutes, which rounds to 4.852 minutes to three decimal places. So the best choice is D.

Solve the Problem. -The Time (In Minutes) a Customer Must Wait in Line