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 54 78 47 3 (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.) μ σ

Answer 1

Answer:

Given that,

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 yrs)	114
1-5	54
6-10	78
11-15	47
16-20	3

(a).

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

x		#	Probability or P(x)	xP(x)	P(x)
0.5	0.25	114	114/299=0.381	0.191	0.095
3	9	57	57/299=0.191	0.573	1.719
8	64	78	78/299=0.261	2.088	16.704
13	169	47	47/299=0.157	2.041	26.533
18	324	3	3/299=0.010	0.18	3.24
Total		=299	P(x)=1	xP(x)=5.073	P(x)=48.291

Expected value or Mean:

Expected value or Mean==E(X)==5.073

Therefore E(X)=5.073

(b).

Find the expected age of a moose killed by a wolf and the standard deviation of the ages. (Use 2 decimal places.):

Variance ():

=48.291-25.735

=22.556

Therefore, Variance V(X)=22.556

Standard Deviation ():

=4.749316

=4.75(Approximately)

Therefore, Standard Deviation ()=4.75.