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 a. Exactly 24 of them survive their first year of life.  b. At most 25 of them survive their first year of life.  c. At least 23 of them survive their first year of life.

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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

a. Exactly 24 of them survive their first year of life. 
b. At most 25 of them survive their first year of life. 
c. At least 23 of them survive their first year of life. 

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Step 1

Given Information:

75% of all bald eagles survive their first year of life. i.e., p=0.75

If n=30 bald eagles are randomly selected, to 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 of bald eagles that survive their first year of life and X follows Binomial distribution with number of trials n=30 and probability of success p=0.75.

Probability mass function of Binomial variable is given by the formula:

PX=x=Cxnpx1-pn-x

Required probability is obtained as follows:

PX=24=C24300.75241-0.7530-24=593775×0.001003391278×0.000244140625=0.14545621490.1455

 

 

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