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In: Statistics and Probability

A warehouse receives orders for a particular product on a regular basis. When an order is...

A warehouse receives orders for a particular product on a regular basis. When an order is placed, customers can order 3, 4, 5, ..., 21 units of the product. Historical data suggest that the size of any given order is equally likely to be of any of these sizes. Let X denote the size of an order.

Find the probability that a customer orders at least five units.

Solutions

Expert Solution

Historical data suggest that the size of any given order is equally likely to be of any of these sizes.

Then, X will follow discrete uniform distribution with range (3, 21). The PMF of X is,

P(X = k) = 1/(21-3 + 1) = 1/19 for k = 3,4, ..., 21

Probability that a customer orders at least five units = P(X 5) = 1 - P(X < 5)

= 1 - P(X 4)

= 1 - [P(X = 3) + P(X = 4)]

= 1 - [1/19 + 1/19]

= 1 - 2/19

= 17/19

orchestra answered 2 years ago
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