# Yearly demand distribution with monthly demand given

Currently working on this problem.

Monthly demand of a product has been observed to follow a normal distribution with mean of $$50$$ pieces and standard deviation of $$5$$ pieces. Assume each month is independent of other months.

1. What is the distribution followed by the yearly demand and what is the mean and standard deviation of that distribution?

I think the distribution remains normal and mean is $$600$$ but how can I calculate the standard deviation?

1. If the store has $$220$$ pieces in stock what is the probability it will cover the demand of the next $$4$$ months?

for that $$4$$ months mean $$= 4*50 =200$$; standard deviation $$= sqrt(4*25) =10$$ ; $$P(X<220)= P(Z<220-200/10)$$

1. How many pieces should the store have to cover the full year's demand ($$12$$ months) with a probability at least equal to $$93,7\%$$ without having to restock?

And this is where my problem begins. I know I need the standard deviation from 1. but even if I had that I can't think of how to incorporate the minimum probability.Can anyone help me?

## 1 Answer

Hints:

In your answer to 2, you say for $4$ months "standard deviation $= sqrt(4*25)$" which supposes each month is independent of other months. If that is true, then you could do the same for a year and say the standard deviation for the year ($12$ months) is $\sqrt{12 \times 25}$.

The method for 3 is in a sense the reverse of that used for 2.

• Silly me. For some reason I had it stuck in my head that for the year I needed a different approach than the one I had already used. It didn't even occur to me to do it like that. Also the months are independent and I forgot to add that. Will edit now
– apot
Commented Dec 6, 2015 at 23:46