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	107 45 74 64 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

Solution:

Given:

Age of Moose in Years	Number Killed by Wolves
Calf (0.5 yr)	107
01-05	45
06-10	74
11-15	64
16-20	6
	N = 296

Part a) For each age group, compute the probability that a moose in that age group is killed by a wolf.

Divide each frequency by total frequency N = 296

Age of Moose in Years	P(x)
Calf (0.5 yr)	0.361
01-05	0.152
06-10	0.250
11-15	0.216
16-20	0.020

Part 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.

Expected age:

Standard Deviation

x	P(x)	x*P(x)	x^2 *P(x)
0.5	0.361	0.18074	0.09037
3	0.152	0.45608	1.36824
8	0.250	2.00000	16.00000
13	0.216	2.81081	36.54054
18	0.020	0.36486	6.56757

Expected age:

Standard Deviation

thus