Question

The weekly demand for an item in a retail store follows a uniform distribution over the range 70 to 83. What would be the weekly demand if its corresponding computer-generated value is 0.5?

Answer 1

Weekly demand will be 76.5

Explanation:

Let X denote the weekly demand for an item

We have given that X follows a uniform distribution with a = 70 and b = 83

So
`f(X)=(1)/(83-70)=(1)/(13)`

Now we need to find
`x_0` such that
`P(X\leq x_0)=0.5`

`\oint_(70)^(x_0)f(x)dx=0.5`

`\oint_(70)^(x_0)(1)/(13)dx=0.5`

`(x_0-70)/(13)=0.5`

`x_0=76.5`

So weekly demand will be 76.5