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 16-20 106 52 77 56 5 (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 Incorrect: Your answer is incorrect. 1-5 Incorrect: Your answer is incorrect. 6-10 Incorrect: Your answer is incorrect. 11-15 Incorrect: Your answer is incorrect. 16-20 Incorrect: Your answer is incorrect. (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 = Incorrect: Your answer is incorrect. σ = Incorrect: Your answer is incorrect.

Answer 1

a)

0.5	0.358
1-5	0.176
6-10	0.260
11-15	0.189
16-20	0.017

b)

x	P(x)	xP(x)	x2P(x)
0.5	0.358	0.179	0.090
3	0.176	0.527	1.581
8	0.260	2.081	16.649
13	0.189	2.459	31.973
18	0.017	0.304	5.473
	total	5.551	55.765
	E(x) =μ=	ΣxP(x) =	5.5507
	E(x2) =	Σx2P(x) =	55.7652
	Var(x)=σ2 =	E(x2)-(E(x))2=	24.955
	std deviation=	σ= √σ2 =	4.9955

μ=5.55

σ= 5.00