Suppose that wait times for customers at a grocery store cashier line are unifor

Question

Suppose that wait times for customers at a grocery store cashier line are uniformly distributed between two minutes and nine minutes.

(a) What are the mean and variance of the waiting time?

(b) What is the probability that a customer waits less than six minutes?

(c) What is the probability that a customer waits between five and ten minutes?

(d) Suppose that a customer who waits k minutes in line receives a coupon worth a 2(k^(1/2)) dollar discount on a future visit. What is the mean of the coupon value for a customer?

Explanation / Answer

PDF of Uniform Distribution f(x) = 1 / ( b - a ) for a < x < b
b = Maximum Value
a = Minimum Value
Mean = a + b / 2
Standard Deviation = Sqrt ( ( b - a ) ^ 2 / 12 )
f(x) = 1/(b-a) = 1 / (9-2) = 1 / 7 = 0.1429
a.
Mean = a + b / 2 = 5.5
Standard Deviation = Sqrt ( ( b - a ) ^ 2 / 12 ) = 2.021
b.
P(X < 6) = (6-2) * f(x)
= 4*0.1429
= 0.572
c.
To find P(a < X < b) =( b - a ) * f(x)
P(5 < X < 10) = (10-5) * f(x)
= 5*0.1429
= 0.715

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