60% of all bald eagles survive their first year of life. Give your answers as decimals, not percents.  If 42 bald eagles are randomly selected, find the probability that a. Exactly 24 of them survive their first year of life.  b. At most 27 of them survive their first year of life.  c. At least 26 of them survive their first year of life.

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60% of all bald eagles survive their first year of life. Give your answers as decimals, not percents.  If 42 bald eagles are randomly selected, find the probability that

a. Exactly 24 of them survive their first year of life. 
b. At most 27 of them survive their first year of life. 
c. At least 26 of them survive their first year of life. 
d. Between 24 and 29 (including 24 and 29) of them survive their first year of life.

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Step 1

Given Information:

60% of all bald eagles survive their first year of life. p=0.60

 If n = 42 bald eagles are randomly selected, find the probability that:

(a) Exactly 24 of them survive their first year of life. 

Let X be a random variable which denotes the number if bald eagles that survive their first year of life and X follows Binomial distribution with parameters n=42 and p=0.60

Binomial formula:

PX=x=Cxnpx1-pn-x

Required probability is obtained as follows:

PX=24=C24420.60241-0.6042-24=(3.536971211×1011)4.738381338×10-66.871947674×10-8=0.11517053330.1152

Thus, the probability that exactly 24 of them survive their first year of life is 0.1152

 

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