Question

65% of all bald eagles survive their first year of life. If 37 bald eagles are randomly selected, find the probability that

a. Exactly 22 of them survive their first year of life.
b. At most 25 of them survive their first year of life.
c. At least 24 of them survive their first year of life.  
d. Between 19 and 26 (including 19 and 26) of them survive their first year of life.

Answer 1

Answer:

Given ,

p = 0.65,

n = 37

a)

To determine probability that exactly 22 of them survive their first year of life

we know,

Binomial Formula = nCr*p^r*q^(n-r)

P(X = 22) = 37C22*(0.65^22)*(0.35^15)

= 9364199760*1.1095*10^-11

= 0.1039

b)

To determine the probability that at most 25 of them survive their first year of life

P(X <= 25) = 37C25*0.65^25*0.35^12

= 0.1316

c)

To determine probability at least 24 of them survive their first year of life

P(X >= 24) = 37C24*0.65^24*0.35^13

= 0.1363

d)To determine required probability

P(19 <= X <= 26) = P(19)+P(20)+P(21)+P(22)+P(23)+P(24)+P(25)+P(26)

= 0.0306+0.0512+0.0769+0.1039+0.1258+0.1363+0.1316+0.1128

P(19 <= X <= 26) = 0.7691