Answered: 60% of all bald eagles survive their…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

Concept explainers

Question

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.

Expert Solution

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:

$P (X = x) = {}^{n}C_{x} p^{x} {(1 - p)}^{n - x}$

Required probability is obtained as follows:

$\begin{array}{rcl} P (X = 24) & = & {}^{42}C_{24} {(0.60)}^{24} {(1 - 0.60)}^{42 - 24} \\ = & (3.536971211 \times 10^{11}) (4.738381338 \times 10^{- 6}) (6.871947674 \times 10^{- 8}) \\ = & 0.1151705333 \\ \approx & 0.1152 \end{array}$

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

Trending now

This is a popular solution!

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Point Estimation, Limit Theorems, Approximations, and Bounds$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.

Similar questions