Question

7. A store is expecting n deliveries between the hours of noon and 1 p.m. Suppose...

7. A store is expecting n deliveries between the hours of noon and 1 p.m. Suppose the arrival time of each delivery truck is uniformly distributed on this 1-hour interval and that the times are independent of one another.

a) What percentage of the time the latest delivery arrives after 12:50?

b) What percentage of the time the first delivery arrives before 12:10?

Math   Statistics-And-Probability   
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Homework Answers

Answer #1

Let X denotes arrival time of each delivery.

Since the arrival time of each delivery truck is uniformly distributed on 1 hour interval.

i.e. X ~ U ( 0,60) , one hour interval contain 60 minutes.

The probability distribution of X is

and the cumulative distribution function is

Let X(i) denote the arrival time of ith delivery truck.

n = expected number of deliveries arrive.

a) Let X(n) : arrival time of latest delivery.

X(n) = maximum order statistic.

The probability distribution of maximum order statistic is

Required Percentage = P ( X(n) > 50)

b) Let X(1) : arrival time of first delivery.

X(1) = first order statistic.

The probability distribution of first order statistic is

Required Probability = P ( X(1) < 10)

.

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