A particular fruit's weights are normally distributed, with a mean of 200 grams and a standard deviation of 30 grams. The heaviest 4% of fruits weigh more than how many grams? Give your answer to the nearest gram.
A particular fruit's weights are normally distributed, with a mean of 200 grams and a standard deviation of 30 grams. The heaviest 4% of fruits weigh more than how many grams? Give your answer to the nearest gram.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
![**Question 5**
A particular fruit's weights are normally distributed, with a mean of 200 grams and a standard deviation of 30 grams.
The heaviest 4% of fruits weigh more than how many grams?
Give your answer to the nearest gram.
[Text Box for Answer]
**Submit Question Button**
**Explanation**
This problem involves understanding the properties of a normal distribution. Here, the mean weight of the fruit is given as 200 grams, and the standard deviation is 30 grams.
To find the weight that separates the heaviest 4% of the fruits, you'll need to determine the z-score that corresponds to the top 4% of a standard normal distribution (a z-score that leaves 96% to the left). This will likely require using a z-table or statistical software to find the exact value. Once you have the z-score, you can use it in the z-score formula to find the corresponding weight.
**Formula for Calculating the Weight Using Z-score:**
\[ X = \mu + (Z \times \sigma) \]
Where:
- \( X \) is the weight you’re solving for.
- \( \mu \) is the mean (200 grams).
- \( Z \) is the z-score.
- \( \sigma \) is the standard deviation (30 grams).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa3129841-f096-4268-a8b3-3e40e7904642%2Fe98f3a13-0e23-4afe-a39c-74cc2d712a09%2Fqqoxkng.jpeg&w=3840&q=75)
Transcribed Image Text:**Question 5**
A particular fruit's weights are normally distributed, with a mean of 200 grams and a standard deviation of 30 grams.
The heaviest 4% of fruits weigh more than how many grams?
Give your answer to the nearest gram.
[Text Box for Answer]
**Submit Question Button**
**Explanation**
This problem involves understanding the properties of a normal distribution. Here, the mean weight of the fruit is given as 200 grams, and the standard deviation is 30 grams.
To find the weight that separates the heaviest 4% of the fruits, you'll need to determine the z-score that corresponds to the top 4% of a standard normal distribution (a z-score that leaves 96% to the left). This will likely require using a z-table or statistical software to find the exact value. Once you have the z-score, you can use it in the z-score formula to find the corresponding weight.
**Formula for Calculating the Weight Using Z-score:**
\[ X = \mu + (Z \times \sigma) \]
Where:
- \( X \) is the weight you’re solving for.
- \( \mu \) is the mean (200 grams).
- \( Z \) is the z-score.
- \( \sigma \) is the standard deviation (30 grams).
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps
Recommended textbooks for you
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
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
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
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
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
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
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman