Question

Bus waiting time is uniformly distributed with the shortest and the longest waiting times being 7 and 38 minutes respectively. What is the standard deviation of the average waiting time of 57 passenger

Answer 1

Answer:

Given that,

Bus waiting time is uniformly distributed with the shortest and the longest waiting times being 7 and 38 minutes respectively.

What is the standard deviation of the average waiting time of 57 passengers:

Here we are given

X Unif(7, 38)

=(1/31)[722-24.5]

=0.0323(697.5)

E(x)=22.52925 (Approximately)

Now,

=(1/31)[18290.6667-114.3333]

=0.0323(18176.3334)

E(x^2)=587.0956(Approximately)

Then,

(Approximately)

So now n=57

Then,

The standard deviation of average =

= 1.1812

Therefore, the standard deviation of the average waiting time of 57 passengers is 1.1812.