Homework Help is Here – Start Your Trial Now!
Math
Statistics
You know that buffaloes have adult weights that are distributed by B = N(2000,200) where the given mean and standard deviation is in Ibs. You inherit a baby buffalo. Find the probability that your buffalo grows up to be at least 1990 pounds. Find the probability that your buffalo will eventually weigh between 1950 and 2100 lbs. |How much would your buffalo have to weigh in order to outweigh 98% of all grown buffalo.

You know that buffaloes have adult weights that are distributed by B = N(2000,200) where the given mean and standard deviation is in Ibs. You inherit a baby buffalo. Find the probability that your buffalo grows up to be at least 1990 pounds. Find the probability that your buffalo will eventually weigh between 1950 and 2100 lbs. |How much would your buffalo have to weigh in order to outweigh 98% of all grown buffalo.

MATLAB: An Introduction with Applications
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
icon
Related questions
Question
### Understanding Buffalo Weights: A Probability Problem **Overview:** You are provided with information about the weights of adult buffalo, which follow a normal distribution. The distribution is given as \( B = N(2000, 200) \), where the mean is 2000 lbs and the standard deviation is 200 lbs. You have inherited a baby buffalo and need to determine various probabilities related to its adult weight. **Questions:** 1. **Probability of Weighing 1990 Pounds or More:** - **Question:** What is the probability that your buffalo grows up to be at least 1990 pounds? - **Approach:** Use the properties of the normal distribution to calculate the probability of the buffalo's weight being greater than or equal to 1990 lbs. 2. **Probability of Weighing Between 1950 and 2100 Pounds:** - **Question:** Find the probability that your buffalo will eventually weigh between 1950 and 2100 pounds. - **Approach:** Calculate the probability that the buffalo's weight falls within this range by finding the cumulative distribution function (CDF) values at 1950 lbs and 2100 lbs, then subtracting them. 3. **Weight to Outweigh 98% of Buffalo:** - **Question:** How much would your buffalo have to weigh in order to outweigh 98% of all grown buffalo? - **Approach:** Determine the weight corresponding to the 98th percentile of the distribution, using the inverse of the cumulative distribution function. **Diagram/Graph Explanation:** While the text provides no direct diagrams or graphs, understanding the normal distribution's bell curve is essential. The curve is centered at the mean (2000 lbs), with the spread determined by the standard deviation (200 lbs). Calculations will involve finding areas under this curve corresponding to the given weight thresholds.
Transcribed Image Text:### Understanding Buffalo Weights: A Probability Problem **Overview:** You are provided with information about the weights of adult buffalo, which follow a normal distribution. The distribution is given as \( B = N(2000, 200) \), where the mean is 2000 lbs and the standard deviation is 200 lbs. You have inherited a baby buffalo and need to determine various probabilities related to its adult weight. **Questions:** 1. **Probability of Weighing 1990 Pounds or More:** - **Question:** What is the probability that your buffalo grows up to be at least 1990 pounds? - **Approach:** Use the properties of the normal distribution to calculate the probability of the buffalo's weight being greater than or equal to 1990 lbs. 2. **Probability of Weighing Between 1950 and 2100 Pounds:** - **Question:** Find the probability that your buffalo will eventually weigh between 1950 and 2100 pounds. - **Approach:** Calculate the probability that the buffalo's weight falls within this range by finding the cumulative distribution function (CDF) values at 1950 lbs and 2100 lbs, then subtracting them. 3. **Weight to Outweigh 98% of Buffalo:** - **Question:** How much would your buffalo have to weigh in order to outweigh 98% of all grown buffalo? - **Approach:** Determine the weight corresponding to the 98th percentile of the distribution, using the inverse of the cumulative distribution function. **Diagram/Graph Explanation:** While the text provides no direct diagrams or graphs, understanding the normal distribution's bell curve is essential. The curve is centered at the mean (2000 lbs), with the spread determined by the standard deviation (200 lbs). Calculations will involve finding areas under this curve corresponding to the given weight thresholds.
Expert Solution
steps

Step by step

Solved in 4 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman
SEE MORE TEXTBOOKS