Question

The time it takes a bank teller to serve a customer is uniformly distributed
between 2 and 6 minutes. A customer has just stepped up to the window,
and you are next in line.

a. What is the expected time you will wait before it is your turn to
be served?
b. What is the probability that you wait less than 1 minute before
being served?
c. What is the probability that you wait between 3 and 5 minutes before
being served?

Answer 1

Solution :

Given that,

a = 2

b = 6

(a)expected value = (a + b) / 2 = (2+6)/2 =4

(b)P(x < c) = (c - a) / (b - a)

P(x < 1) = (1 - 2) / (6 - 2) = 0.25

Probability = 0.25

(c)P(c < x < d) = (d - c) / (b - a)

P(3 < x < 5) = (5 - 3) / (6 - 2 ) = 0.5

Probability = 0.5