Question

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 exactly five units.

A warehouse receives orders for a particular product on a regular basis. When an order is placed, customers can order 3, 4, 5, ..., 25 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 most five units.

A warehouse receives orders for a particular product on a regular basis. When an order is placed, customers can order 3, 4, 5, ..., 22 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.

Answer 1

Answer of first question:

Let X denote the sixe of order. Then X can take values 3,4,....,21. Since the size of any given order is equally likely, then the probability that a customer will order product of size x is given by

P(X=x)=1/18 ; x=3,4,....,21

Then the probability that a customer orders exactly five units(size of order is 5), is given by

P(X=5) = 1/18.

Answer of second question:

Let X denote the sixe of order. Then X can take values 3,4,....,25. Since the size of any given order is equally likely, then the probability that a customer will order product of size x is given by

P(X=x)=1/23 ; x=3,4,....,25.

Then the probability that a customer orders atmost five units, is given by

Answer of third question:

Let X denote the sixe of order. Then X can take values 3,4,....,22. Since the size of any given order is equally likely, then the probability that a customer will order product of size x is given by

P(X=x)=1/20 ; x=3,4,....,22.

Then the probability that a customer orders at least five units, is given by