Whether it is surprising for more than 4 elk in

sjeikdom0

sjeikdom0

Answered question

2021-09-28

Whether it is surprising for more than 4 elk in the sample to survive to adulthood and calculate an appropriate probability.
Given information:
Number of trials, n=7
Probability of success, p=44%=0.44

Answer & Explanation

Lacey-May Snyder

Lacey-May Snyder

Skilled2021-09-29Added 88 answers

Calculations:
According to the binomial probability,
P(X=k)=(nk)pk(1p)nk
Addition rule for mutually exclusive event:
P(AB)=P(A or B)=P(A)+P(B)
At k=5,
The binomial probability to be evaluated as:
P(X=5)=(75)(0.44)5(10.44)75
=7!5!(75)!(0.44)5(0.56)2
=21(0.44)5(0.56)2
0.1086
At k=6,
The binomial probability to be evaluated as:
P(X=6)=(76)(0.44)6(10.44)76
=7!6!(76)!(0.44)6(0.56)1
=7(0.44)6(0.56)1
0.0284
At k=7,
The binomial probability to be evaluated as:
P(X=7)=(77)(0.44)7(10.44)77
=7!7!(77)!(0.44)7(0.56)0
=1(0.44)7(0.56)0
0.0032
Since two different numbers of successes are impossible on same simulation.
Apply addition rule for mutually exclusive events:
P(X>4)=P(X=5)+P(X=6)+P(X=7)
=0.1086+0.0284+0.0032
=0.1402
The probability less than 0.05 is considered to be small.
But in this case,
The probability is not small.
This implies
The event is likely to occur by chance.
Thus,
The event of more than 4 elk surviving to adulthood is not surprising.

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