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 16-20 114 55 73 50 4 (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 .385 Correct: Your answer is correct. 1-5 .186 Correct: Your answer is correct. 6-10 .247 Correct: Your answer is correct. 11-15 .169 Correct: Your answer is correct. 16-20 .014 Correct: Your answer is correct. (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)

Following table shows the calculations:

Age of Moose in Years	Number killed by Wolves, f	Probability, f/296
0.5	114	0.385
1-5	55	0.186
6-10	73	0.247
11-15	50	0.169
16-20	4	0.014
Total	296	1

(b)

Following table shows the calculations:

Midpoint, x	P(X=x)	xP(X=x)	x^2*P(X=x)
0.5	0.385	0.1925	0.09625
3	0.186	0.558	1.674
8	0.247	1.976	15.808
13	0.169	2.197	28.561
18	0.014	0.252	4.536
Total		5.1755	50.67525

The mean is:

The standard deviation is: