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

Answer:

Weekly demand will be 76.5

Step-by-step 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 $f(X)=\frac{1}{83-70}=\frac{1}{13}$

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

$\oint_{70}^{x_0}f(x)dx=0.5$

$\oint_{70}^{x_0}\frac{1}{13}dx=0.5$

$\frac{x_0-70}{13}=0.5$

$x_0=76.5$

So weekly demand will be 76.5