75% of all bald eagles survive their first year of

Rui Baldwin

Rui Baldwin

Answered question

2021-09-27

75% of all bald eagles survive their first year of life. Give your answers as decimals, not percents. If 30 bald eagles are randomly selected, find the probability that.
Between 20 and 26 (including 20 and 26) of them survive their first year of life.

Answer & Explanation

SabadisO

SabadisO

Skilled2021-09-28Added 108 answers

Step 1
The Binomial probability distribution is:
P(X=x)=(nx)(p)x(1p)nx
In the formula, n denotes the number of trails, p denotes probability of success, and x denotes the number of success.
Let x denotes the the number of bald eagles survive their first year of life which follows binomial with sample size 30 and probability of success is 0.75.
Step 2
The probability that Between 20 and 26 (including 20 and 26) of them survive their first year of life is,
P(20X26)=P(X=20)+P(X=21)+P(X=22)+P(X=23)+P(X=24)+P(X=25)=P(X=26)
=(3020)(0.75)20(10.75)3020+(3021)(0.75)21(10.75)3021++(3026)(0.75)26(10.75)3026
=0.0909+0.1298+0.1593+0.1662+0.1454+0.1047+0.0604
=0.8567
Thus, the probability that Between 20 and 26 (including 20 and 26) of them survive their first year of life is 0.8567.

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