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 51 75 57 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.)

Answer 1

Solution:

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

To find probability divide each frequency by total frequency.

Thus we get:

Age of Moose in Years	Number Killed by Wolves	Calculations
Calf (0.5 yr)	107	=107/296
1 --5	51	=51/296
6--10	75	=75/296
11--15	57	=57/296
16--20	6	=6/296
	296

Age of Moose in Years	Probability
Calf (0.5 yr)	0.361
1 --5	0.172
6--10	0.253
11--15	0.193
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.

thus

Age of Moose in Years	Probability	x:mid points	x*P(x)	x^2*P(x)
Calf (0.5 yr)	0.361	0.5	0.1807	0.0904
1 --5	0.172	3	0.5169	1.5507
6--10	0.253	8	2.0270	16.2162
11--15	0.193	13	2.5034	32.5439
16--20	0.020	18	0.3649	6.5676

Thus

Mean ( Expected Value)

and

Standard deviation:

where

thus