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In: Statistics and Probability

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

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

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Expert Solution

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.

orchestra answered 1 year ago

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