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.
- 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?
- 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 $= sqrt(4*25) =10$ ; $P(X<220)= P(Z<220-200/10)$
- 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?
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.