Question

The amount of time, in minutes that a person must wait for a bus is uniformly distributed between 4 and 16.5 minutes, X~U(4, 16.5).

a.) Find the mean of this uniform distribution.

b.) Find the standard deviation of this uniform distribution.

c.) If there are 16 people waiting for the bus and using the central limit theorem, what is the probability that the average of 16 people waiting for the bus is less than 8 minutes?

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Answer 1

Solution

The amount of time, in minutes that a person must wait for a bus is uniformly distributed between 4 and 16.5 minutes, X~U(4, 16.5)

let a =4, b= 16.5

a.) Find the mean of this uniform distribution.

Mean = (a+b) / 2

Mean = (4+16.5)/2

Mean = 10.25

b.) Find the standard deviation of this uniform distribution

standard deviation =

standard deviation =

standard deviation =3.6083

c.) If there are 16 people waiting for the bus and using the central limit theorem, what is the probability that the average of 16 people waiting for the bus is less than 8 minutes?