Question

In: Statistics and Probability

Isle Royale, an island in Lake Superior, has provided an important study site of wolves and...

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.)

Solutions

Expert Solution

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


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