Question

Suppose the waiting time for a bus is uniformly distributed between 10 and 20 minutes. calculate the 80th percentile of the waiting time for the bus.

a) 12 minutes
b) 15 minutes
c) 18 minutes
d) 20 minutes

Answer 1

The 80th percentile of a bus waiting time that is uniformly distributed between 10 and 20 minutes is calculated using the properties of the uniform distribution and is found to be 18 minutes.

Step-by-step explanation:

To find the 80th percentile of the waiting time for a bus that is uniformly distributed between 10 and 20 minutes, we utilize the properties of the uniform distribution. The formula for any percentile in a uniform distribution is given by:

P(X) = a + (b - a) * (percentile / 100)

For the 80th percentile, this becomes:

P(X) = 10 + (20 - 10) * (80 / 100)

P(X) = 10 + 10 * 0.8

P(X) = 10 + 8

P(X) = 18

Therefore, the 80th percentile of the waiting time is 18 minutes, which corresponds to option c.

Answer 2

The 80th percentile of the waiting time for the bus is 18 minutes.

Therefore, the correct answer is c) 18 minutes.

The 80th percentile of a uniform distribution between a and b can be calculated using the formula:

P_80 =a+0.8⋅(b- a)

In this case,

a=10 minutes and b=20 minutes.

P_80​ =10+0.8⋅(20−10)

P_80 =10+0.8⋅10

P_80​ =10+8

P_80 =18

So, the 80th percentile of the waiting time for the bus is 18 minutes.

Therefore, the correct answer is:

c) 18 minutes