Question

Q1.         You are promoted to Marketing Manager in the cell phone manufacturing company. Your are responsible for the analysis of warranty data. Warranty claims record the number of years to failure. From the following table , develop the yearly probabilities to failure. Let x in the table represent the number of years in which a cell phone failed and p(x) the calculated probability of failure. Roud to 4 decimal places

X                             p(x)

4                              0.02

5                              0.07

6                              0.15       

7                              0.30

8                              0.46

Calculate the expected value?

What is the calculated variance?

What is the calculated standard Deviation?

Answer 1

Solution:

x	P(x)	x * P(x)	x2 * P(x)
4	0.02	0.08	0.32
5	0.07	0.35	1.75
6	0.15	0.9	5.4
7	0.3	2.1	14.7
8	0.46	3.68	29.44
Sum	1	7.11	51.61

Mean = X * P(X)

= 7.11

Variance =

= X 2 * P(X) - 2

= 51.61 - (7.11)2 = 1.0579

Standard deviation = = 1.0285