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?
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
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