Question

8 0.05 10 0.05 13 0.17 0.16 15 0.17 20 02 21 23 0.1 00 0.0 0.0 a) P(x > 10) b) P(x>10) c) P(x < 20) d) P(x = 8 or x = 10) e) The mean for variable x f) The standard deviation for variable x. 3. 2 IX P(x) 30 6 0.16 10 0.05 11 0.05 16 0.1 20 0.2 25 0.1 0.2 a) P(x>6) b) P(x211) c) P(x < 10) d) Pix = 11 or x = 10)

Answer 1

a) P(X>10) =0.1+0.1+0.2+0.1+0.2 =0.7

b)P(X>=10)=0.05+0.1+0.1+0.2+0.1+0.2 =0.75

c) P(X<20) =0.04+0.16+0.05+0.05+0.1+0.1 =0.5

d) P(X=8 or X=10) =0.05+0.05 =0.10

e)

x	f(x)	xP(x)	x2P(x)
5	0.0400	0.2000	1.0000
6	0.1600	0.9600	5.7600
8	0.0500	0.4000	3.2000
10	0.0500	0.5000	5.0000
13	0.1000	1.3000	16.9000
15	0.1000	1.5000	22.5000
20	0.2000	4.0000	80.0000
21	0.1000	2.1000	44.1000
23	0.2000	4.6000	105.8000
	total	15.5600	284.2600
	E(x) =μ=	ΣxP(x) =	15.5600
	E(x2) =	Σx2P(x) =	284.2600
	Var(x)=σ2 =	E(x2)-(E(x))2=	42.1464
	std deviation=	σ= √σ2 =	6.4920

from above mean =15.56

f)

standard deviation =6.4920

3)

for P(X=2)=1-0.16-0.05-0.05-0.1-0.2-0.1-0.2 = 0.14

a)

P(X>6) =0.05+0.05+0.1+0.2+0.1+0.2 =0.65

b)P(X>=11) =0.05+0.1+0.2+0.1+0.2 =0.65

c)

P(X<10) =0.14+0.16 =0.30

d)P(X=11 or x=10) =0.05+0.05 =0.1

x	f(x)	xP(x)	x2P(x)
2	0.1400	0.2800	0.5600
6	0.1600	0.9600	5.7600
10	0.0500	0.5000	5.0000
11	0.0500	0.5500	6.0500
16	0.1000	1.6000	25.6000
20	0.2000	4.0000	80.0000
25	0.1000	2.5000	62.5000
30	0.2000	6.0000	180.0000
	total	16.3900	365.4700
	E(x) =μ=	ΣxP(x) =	16.3900
	E(x2) =	Σx2P(x) =	365.4700
	Var(x)=σ2 =	E(x2)-(E(x))2=	96.8379
	std deviation=	σ= √σ2 =	9.8406

e) expected value =16.39

f)

standard deviation =9.8406