Question 1200130: 72% of all bald eagles survive their first year of life. Give your answers as decimals, not percents. If 34 bald eagles are randomly selected, find the probability that
a. Exactly 26 of them survive their first year of life_______
b. At most 26 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 by textot(100)   (Show Source):
You can put this solution on YOUR website! **a) Exactly 26 of them survive their first year of life**
* This is a binomial probability problem.
* **n = 34** (number of trials - eagles)
* **p = 0.72** (probability of success - survival)
* **x = 26** (number of successes)
* **Formula:** P(X = x) = (nCx) * p^x * (1-p)^(n-x)
* where nCx = n! / (x! * (n-x)!)
* **Calculation:**
* P(X = 26) = (34C26) * (0.72)^26 * (0.28)^(34-26)
* P(X = 26) ≈ 0.116
**b) At most 26 of them survive their first year of life**
* This means we need to find the probability of 26 or fewer eagles surviving.
* P(X ≤ 26) = P(X = 0) + P(X = 1) + ... + P(X = 26)
* This can be calculated using a binomial probability table, a calculator with a binomial probability function, or statistical software.
* **Using a calculator or software:** P(X ≤ 26) ≈ 0.874
**c) At least 24 of them survive their first year of life**
* This means we need to find the probability of 24 or more eagles surviving.
* P(X ≥ 24) = P(X = 24) + P(X = 25) + P(X = 26) + ... + P(X = 34)
* **Using a calculator or software:** P(X ≥ 24) ≈ 0.878
**d) Between 19 and 26 (including 19 and 26) of them survive their first year of life**
* This means we need to find the probability of 19, 20, 21, ..., 26 eagles surviving.
* P(19 ≤ X ≤ 26) = P(X = 19) + P(X = 20) + ... + P(X = 26)
* **Using a calculator or software:** P(19 ≤ X ≤ 26) ≈ 0.820
**In summary:**
* a) P(X = 26) ≈ 0.116
* b) P(X ≤ 26) ≈ 0.874
* c) P(X ≥ 24) ≈ 0.878
* d) P(19 ≤ X ≤ 26) ≈ 0.820
**Note:** These calculations require the use of a calculator or statistical software with binomial probability functions.
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