Question

Solve the question and show all steps: Consider the probability distribution shown here:

Y	-40	-30	-20	-10	0	10	20	30	40
P(Y)	.02	.07	.10	.15	.30	.18	.10	.06	.02

a. Calculate E(Y) or µ, VAR(Y) or ? 2 , and STDV(Y) or σ

b. Graph P(Y). Locate µ, µ - 2σ, and µ + 2σ on the graph

c. What is the probability that Y is in the interval ? ± 2??

Answer 1

Y	P(Y)	Y*P(Y)
-40	0.02	-0.8	32
-30	0.07	-2.1	63
-20	0.1	-2	40
-10	0.15	-1.5	15
0	0.3	0	0
10	0.18	1.8	18
20	0.1	2	40
30	0.06	1.8	54
40	0.02	0.8	32
			Sum = 294

E(Y) or µ =

VAR(Y) or ?² =

STDV(Y) or σ =

µ - 2σ = 0 - 2*17.146 = -34.292

µ + 2σ = 0 + 2*17.146 = 34.292

b.)

c.) probability that Y is in the interval ? ± 2? = 95% [Using Emperical rule of Std. Dev.]  

Note:- Empirical Rule of Standard Deviation:

–Applied on Bell-shaped data

–68% data lies within ±1σ of the mean

–95% data lies within ±2σ of the mean

–99.7% data lies within ±3σ of the mean