Probability- minimum inventory to satisfy demand

[Roni1985]

Homework Statement

There are 20 customer locations, the demand in each location is normal with mean 60 and SD 20. All 20 locations have independent probabilities.
The goal is to cover all of the demand in a month at least 95% of the times. What's the minimum total inventory the company should hold?

Homework Equations

The Attempt at a Solution

It doesn't sound like I need to find the confidence interval. So, I know that the total mean is 1200 and the total standard deviation is 400. So, since the sum is also normal, I just go two SDs to the right to find the 95%.
If I got 2 SDs to the right, I get 2000.

Is this the correct method to use here?

 

[Ray Vickson]

Homework Statement

There are 20 customer locations, the demand in each location is normal with mean 60 and SD 20. All 20 locations have independent probabilities.
The goal is to cover all of the demand in a month at least 95% of the times. What's the minimum total inventory the company should hold?

Homework Equations

The Attempt at a Solution

It doesn't sound like I need to find the confidence interval. So, I know that the total mean is 1200 and the total standard deviation is 400. So, since the sum is also normal, I just go two SDs to the right to find the 95%.
If I got 2 SDs to the right, I get 2000.

Is this the correct method to use here?

G

How do you figure that the total standard deviation is 400? I get something very different.

RGV

 

[Roni1985]

G

How do you figure that the total standard deviation is 400? I get something very different.

RGV

oh shoot, that's the variance I guess.
so, SD is just 20.

But, now I'm thinking maybe I should use the gaussian pdf...?
EDIT:
I used excel's =NORMINV(0.975,1200,20)
And I get 1240 both ways... so I think its good.
But if wanted to use the gaussian pdf, how would you calculate it?

 

[Ray Vickson]

oh shoot, that's the variance I guess.
so, SD is just 20.

But, now I'm thinking maybe I should use the gaussian pdf...?
EDIT:
I used excel's =NORMINV(0.975,1200,20)
And I get 1240 both ways... so I think its good.
But if wanted to use the gaussian pdf, how would you calculate it?

(i) You still don't have the correct standard deviation.

(ii) Where does the 0.975 come from?

RGV

 

[Roni1985]

Ya I'm a lil rusty
it's sqrt(20)*20
and the prob is just .95

 

[Ray Vickson]

Ya I'm a lil rusty
it's sqrt(20)*20
and the prob is just .95

Right!

RGV