Question

Isle Royale, an island in Lake Superior, has provided an important study site of wolves and their prey. Of special interest is the study of the number of moose killed by wolves. In the period from 1958 to 1974, there were 296 moose deaths identified as wolf kills. The age distribution of the kills is as follows. Age of Moose in Years Number Killed by Wolves Calf (0.5 yr) 1-5 6-10 11-15 16-20 111 49 72 58 6 (a) For each age group, compute the probability that a moose in that age group is killed by a wolf. (Round your answers to three decimal places.) 0.5 1-5 6-10 11-15 16-20 (b) Consider all ages in a class equal to the class midpoint. Find the expected age of a moose killed by a wolf and the standard deviation of the ages. (Round your answers to two decimal places.) μ = σ =

Answer 1

a)dividing frequency with total value of 296:

age group		Probability(X=x)
0.5		0.375
1-5		0.166
6-10		0.243
11-15		0.196
16-20		0.020

b)

x	P(X=x)	xP(x)	x2P(x)
0.5	0.375	0.18750	0.09375
3	0.166	0.49662	1.48986
8	0.243	1.94595	15.56757
13	0.196	2.54730	33.11486
18	0.020	0.36486	6.56757
total		5.5422	56.8336
	E(x) =μ=	ΣxP(x) =	5.5422
	E(x2) =	Σx2P(x) =	56.8336
	Var(x)=σ2 =	E(x2)-(E(x))2=	26.117304
	std deviation=	σ= √σ2 =	5.11051

μ = 5.54

σ=5.11