Question

in middle earth, brave warriors come in all shapes and sizes. The following table lists the standardized height of combatants on the left and the frequency of their being present in the army on the right.

0 10

1 50

2 1000

3 300

4 50

a) find the relative frequency, probability (of each category), mean, and standard deviation

b) What is the probability a randomly selected combatant will be from Height class 3 or Height Class 4?

c) What is the probability that a randomly selected combatant will be in at least height class 2?

d) what is the probability that a randomly selected combatant will be at most in height class 3?

Answer 1

a) dividing ech cell with total frequency 1410 ; below is relative frequency table:

x	relative freq
0	0.0071
1	0.0355
2	0.7092
3	0.2128
4	0.0355

x	P(x)	xP(x)	x2P(x)
0	0.0071	0.000	0.000
1	0.0355	0.035	0.035
2	0.7092	1.418	2.837
3	0.2128	0.638	1.915
4	0.0355	0.142	0.567
	total	2.234	5.355
	E(x) =μ=	ΣxP(x) =	2.2340
	E(x2) =	Σx2P(x) =	5.3546
	Var(x)=σ2 =	E(x2)-(E(x))2=	0.364
	std deviation=	σ= √σ2 =	0.6030

from above mean =E(X)=2.2340

and standard deviation =0.6030

b)

probability a randomly selected combatant will be from Height class 3 or Height Class 4

=(300+50)/1410 =0.2482

c)

probability that a randomly selected combatant will be in at least height class 2

=(1000+300+50)/1410 =0.9574

d)

probability that a randomly selected combatant will be at most in height class 3

=(10+50+1000+300)/1410=0.9645