Question

6. Your marketin g department has developed projections of sales levels and their probabilities for the coming year. They need someone to finish the statistical analysis and communicate what it means. 6.1 (10 pts) Fill in this table. 2 20 .3 10 .5 Total 6.2 (5 pts) Calculate ECX). 6.3 (5 pts) Calculate Var(X) and Std Dev. 6.4 (5 pts) Comment on the results.

Answer 1

The probability distribution is given

6.1

P	X	Pi*(Xi)
0.2	20	4	20 - 10 = 10	102 = 100	100 * 0.2 = 20
0.3	10	3	10 - 10 = 0	02 = 0	0 * 0.3 = 0
0.5	6	3	6 - 10 = -4	(-4)2 = 16	16 * 0.5 = 8
Total		10			28

6.2 E(X)

The formula to find the expected value is

Which is also denoted by

Now subtract 10 from each X and then fill the entries in the fourth column.

Take square of fourth column and fill in fifth column.

Multiply fifth column by first and fill in the last column.

6.3 Var(X)

The formula of variance is

(calculated in the last column)

Standard deviation is nothing but the square root of variance.

Std Dev = /Variance= V 28= 5.2915

6.4  

The expected number of sales level by marketing department is 10 in the coming year.

The variation between the sales level is 28 and the standard deviation is 5.2915