Question

The wait time for service at a local DMV is uniformly distributed from 1 minute to 9 minutes. a. Find the probability that a randomly selected person waits 1.5 to 5 minutes. b. Find the expected wait time. c. Find the standard deviation of the wait time.

Answer 1

a) We fin the probability in a random selected person between 1.5 min and 5 min.

1 to 9 is a interval of 8 minutes.

1.5 to 5 is a interval of 3.5

`P(1.5<x<5)=(5-1.5)/(9-1) = (3.5)/(8)=0.4375`

b) With the formula of Expected Value we can find the time, that is

`E(t) = (a+b)/2 = (9+1)/2 =`5 minutes

c) The standar desviation of uniform distribution is given by,

`s= (a-b)/(√(n))`

`s=(9-1)/(√(12))`

`s=2.3094`