Question

1. For the probability distribution below find the mean, variance, and standard deviation.

?	P(?)	?P (?)	?2P(?)
0	0.15
1	0.20
2	0.35
3	0.22
4	0.08

    

2. The probability distribution shows the cups of beer American Adults consume every week. Find the expected value of cups of wine American Adults consume every week.

?	P(?)	?P(?)
0	0.4
1	0.1
2	0.3
5	0.12
10	0.05

Answer 1

(1)

x	P(x)	x * P(x)	x2 * P(x)
0	0.15	0	0
1	0.2	0.2	0.2
2	0.35	0.7	1.4
3	0.22	0.66	1.98
4	0.08	0.32	1.28
Sum	1	1.88	4.86

Mean = = X * P(X) = 1.88   

Variance = X ² * P(X) - ² = 4.86 - 1.88² = 1.3256

Standard deviation = = 1.151347

(2)

x	P(x)	x * P(x)
0	0.4	0
1	0.1	0.1
2	0.3	0.6
5	0.12	0.6
10	0.05	0.5
Sum	0.97	1.8

expected value = = X * P(X) = 0.97