1. ## Sample Probability

The monthly sales of a chocolate company is believed to be normally distributed with a mean of 1,000 bars and a standard deviation of 150 bars.Find the probability that the total sales in the next year is over 12,600 bars with assuming that the sales of the 12 months are independent.

2. Originally Posted by someone21
The monthly sales of a chocolate company is believed to be normally distributed with a mean of 1,000 bars and a standard deviation of 150 bars.Find the probability that the total sales in the next year is over 12,600 bars with assuming that the sales of the 12 months are independent.
Let Y be the random variable sales in 1 year.

You should realise that Y ~ Normal $\displaystyle \left(\mu = (12)(1,000) = 12,000 ~ \sigma^2 = 12 (150^2) = 270,000 \Rightarrow \sigma = 519.6\right)$ (read this: Sum of normally distributed random variables - Wikipedia, the free encyclopedia).

Find Pr(Y > 12,600).

3. Originally Posted by someone21
The monthly sales of a chocolate company is believed to be normally distributed with a mean of 1,000 bars and a standard deviation of 150 bars.Find the probability that the total sales in the next year is over 12,600 bars with assuming that the sales of the 12 months are independent.
Would it be different if the monthly sales of a chocolate company is believed to be normally distributed to exactly normal distributed??

And i still do not understand why we use sampling distributions

So when to use sampling distributions and normal distributions

4. Originally Posted by someone21
Would it be different if the monthly sales of a chocolate company is believed to be normally distributed to exactly normal distributed??

Mr F says: No.

And i still do not understand why we use sampling distributions Mr F says: The idea of sampling distibution is NOt being used here. The distribution of the sum of 12 normal random variables is required. It should be clear from my previous post why this sum is required.

So when to use sampling distributions and normal distributions
..

5. Originally Posted by mr fantastic
Would it be different if the monthly sales of a chocolate company is believed to be normally distributed to exactly normal distributed??

Mr F says: No. But then isn't in approximately(believed) normal distributed meaning the population can be not normal as well

And i still do not understand why we use sampling distributions Mr F says: The idea of sampling distibution is NOt being used here. The distribution of the sum of 12 normal random variables is required. It should be clear from my previous post why this sum is required.

So when to use sampling distributions and normal distributions This is the main question please help like to is there any tips on when to use sampling distributions instead of normal
Thanks