Question

The distribution of GMAT scores in math for an incoming class of business studies has a mean of 620 and standard deviation of 15. Assume that the score are normally distributed. Generate 25 random variates from this distribution as whole numbers. (35 points) The weekly demand of a slow-moving product has the following probability mass function Demand, x Probability, f(x) 0 0.2 1 0.4 2 0.3 3 0.1 4 or more 0 Use VLOOKUP to generate 25 random variates from this distribution. (25 points)

Answer 1

Q1) We are given the distribution here as:

X Nu = 620,0 = 15)

For generating a random number from the above distribution, the random number is computed here by first generating a random number between 0 and 1 and then, for that cumulative probability and above normal distribution parameters, we obtain the random number in EXCEL here as:

=ROUND(NORM.INV(RAND(),620,15),0)

S.No.	Random Number	EXCEL Formula
1	640	=ROUND(NORM.INV(RAND(),620,15),0)
2	625	=ROUND(NORM.INV(RAND(),620,15),0)
3	635	=ROUND(NORM.INV(RAND(),620,15),0)
4	617	=ROUND(NORM.INV(RAND(),620,15),0)
5	620	=ROUND(NORM.INV(RAND(),620,15),0)
6	603	=ROUND(NORM.INV(RAND(),620,15),0)
7	599	=ROUND(NORM.INV(RAND(),620,15),0)
8	616	=ROUND(NORM.INV(RAND(),620,15),0)
9	625	=ROUND(NORM.INV(RAND(),620,15),0)
10	586	=ROUND(NORM.INV(RAND(),620,15),0)
11	628	=ROUND(NORM.INV(RAND(),620,15),0)
12	629	=ROUND(NORM.INV(RAND(),620,15),0)
13	594	=ROUND(NORM.INV(RAND(),620,15),0)
14	598	=ROUND(NORM.INV(RAND(),620,15),0)
15	612	=ROUND(NORM.INV(RAND(),620,15),0)
16	590	=ROUND(NORM.INV(RAND(),620,15),0)
17	601	=ROUND(NORM.INV(RAND(),620,15),0)
18	638	=ROUND(NORM.INV(RAND(),620,15),0)
19	606	=ROUND(NORM.INV(RAND(),620,15),0)
20	623	=ROUND(NORM.INV(RAND(),620,15),0)
21	626	=ROUND(NORM.INV(RAND(),620,15),0)
22	618	=ROUND(NORM.INV(RAND(),620,15),0)
23	610	=ROUND(NORM.INV(RAND(),620,15),0)
24	617	=ROUND(NORM.INV(RAND(),620,15),0)
25	624	=ROUND(NORM.INV(RAND(),620,15),0)

This is the way of creating the random numbers ( nearest whole number ), the formula is given in the last column here.