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

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)                                                   109

1-5                                                          45

6-10                                                           76

11-15                                                         64

16-20                                                            2

(a) For each age group, compute the probability that a moose in that age group is killed by a wolf. (Use 3 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. (Use 2 decimal places.)

Explanation / Answer

The probbailities corresponding to each age groups are as follows:

109/296=0.368, 45/296=0.1520, 76/296=0.2568, 64/296=0.2162, 2/296=0.0068

SD=Summation X^2f-[summation (xf)^2/n]

17414.25-1883.5^2/296

=5429.2086

Mean=fx/n=1883.5/296=6.3632

Midpoint (x) Frequency(f) f*x x^2*f 0-0.5 2.5 109 272.5 681.25 1-5 3 45 135 405 6-10 8 76 608 4864 11-15 13 64 832 10816 16-20 18 2 36 648 1883.5 17414.25

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