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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?

Respuesta :

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 [tex]f(X)=\frac{1}{83-70}=\frac{1}{13}[/tex]

Now we need to find [tex]x_0[/tex] such that [tex]P(X\leq x_0)=0.5[/tex]

[tex]\oint_{70}^{x_0}f(x)dx=0.5[/tex]

[tex]\oint_{70}^{x_0}\frac{1}{13}dx=0.5[/tex]

[tex]\frac{x_0-70}{13}=0.5[/tex]

[tex]x_0=76.5[/tex]

So weekly demand will be 76.5

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