Question

Suppose a retailer has two markets, 1 and 2. demand 1 follows normal distribution with mean 100 and standard deviation 12.4. demand 2 follows normal distribution with mean 110 and standard deviation 16.7. the retailer needs to know the mean and standard deviation of the TOTAL demand. please describe the conceptual analysis process to find out these two parameters by using simulation

Answer 1

D1 = 100

SD1 = 12.4

D2 = 110

SD2 = 16.7

We all know that variance follow additive property, hence the Standard Deviation of Difference = sqrt(SD22 - SD12 )= 11.186

The new Mean will follow the midpoint theorem and hence will be = (D2 - D1)/2 = 5

Let X1 be a point on first Normal Distribution and X2 be a corresponding point on second normal distribution at same z value.

The difference between these two discrete points will be - X2 - X1

Let that difference be X which is equal to X2-X1

We know Z value on a normal curve = (X - Mean)/Std Dev. Thus in our case, Z = (X - 5)/11.186

or X = 11.186*Z + 5

Now Calculate X for all possible values of Z (for simplicity use range -4 to +4 in a period of 0.25)

Obtain the points of normal distribution by using Norm.dist function with above obtained all possible values of X as first argument, Mean of Difference as second, Std Dev of Difference as Thirds and False in fourth for PDF)

Plot the above obtained points of normal distribution with their corresponding Z values and obtain the required difference normal curve.