Question

For a group of four men, the probability for the number, x, who live through the next year is given by

x	P(x)
0	0.045
1	0.015
2	0.1
3	0.55
4	0.29

(a) Find the mean and standard deviation of the number of men in a group of four who will live through the next year.
(b) Find the probability that at least 2 men in a group of four will survive the next year.

(c) Is 1 a significantly low number of men in a group of four to survive the next year? Why or why not?

Answer 1

x	f(x)	xP(x)	x2P(x)
0	0.0450	0.00	0.0000
1	0.0150	0.02	0.0150
2	0.1000	0.20	0.4000
3	0.5500	1.65	4.9500
4	0.2900	1.16	4.6400
	total	3.0250	10.0050
	E(x) =μ=	ΣxP(x) =	3.0250
	E(x2) =	Σx2P(x) =	10.0050
	Var(x)=σ2 =	E(x2)-(E(x))2=	0.8544
	std deviation=	σ= √σ2 =	0.924

a) mean =3.025

standard deviation =0.924

b)

  probability that at least 2 men in a group of four will survive the next year=0.1+0.55+0.29 =0.94

c) No a sprobability of getting 1 or less is (0.045+0.015=0.06) is not less than 0.05 , therefore this is not an unusual event