On a planet far far away from Earth, IQ of the ruling species is normally distributed with a mean of 102 and a standard deviation of 18. Suppose one individual is randomly chosen. Let X = IQ of an individual. a. What is the distribution of X? X - N( b. Find the probability that a randomly selected person's IQ is over 84. Round your answer to 4 decimal places. c. A school offers special services for all children in the bottom 6% for IQ scores. What is the highest IQ score a child can have and still receive special services? Round your answer to 2 decimal places. d. Find the Inter Quartile Range (IQR) for IQ scores. Round your answers to 2 decimal places. Q1: Q3: IQR:
On a planet far far away from Earth, IQ of the ruling species is normally distributed with a mean of 102 and a standard deviation of 18. Suppose one individual is randomly chosen. Let X = IQ of an individual. a. What is the distribution of X? X - N( b. Find the probability that a randomly selected person's IQ is over 84. Round your answer to 4 decimal places. c. A school offers special services for all children in the bottom 6% for IQ scores. What is the highest IQ score a child can have and still receive special services? Round your answer to 2 decimal places. d. Find the Inter Quartile Range (IQR) for IQ scores. Round your answers to 2 decimal places. Q1: Q3: IQR:
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![### Probability and Statistics Practice Problem
On a planet far far away from Earth, the IQ of the ruling species is normally distributed with a mean of 102 and a standard deviation of 18. Suppose one individual is randomly chosen. Let \( X \) = IQ of an individual.
#### Questions:
a. **What is the distribution of \( X \)?**
\( X \sim N(\mu, \sigma^2) \)
\( X \sim N( \_\_\_\_ , \_\_\_\_ ) \)
b. **Find the probability that a randomly selected person's IQ is over 84.**
\(\_\_\_\_\_)
*Round your answer to 4 decimal places.*
c. **A school offers special services for all children in the bottom 6% for IQ scores. What is the highest IQ score a child can have and still receive special services?**
\(\_\_\_\_\_)
*Round your answer to 2 decimal places.*
d. **Find the Interquartile Range (IQR) for IQ scores.**
*Round your answers to 2 decimal places.*
- **Q1:** \(\_\_\_\_\_)
- **Q3:** \(\_\_\_\_\_)
- **IQR:** \(\_\_\_\_\_)
#### Hint:
##### Helpful videos:
- [Find a Probability \[+\]](#)
- [Finding a Value Given a Probability \[+\]](#)
- [Hint \[+\]](#)
---
In case calculations are needed for any of the questions above, make sure to reference appropriate statistical techniques and tables (e.g., Z-tables for standard normal distribution, quartile calculations, etc.).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F77379e33-cd78-4bf1-a88e-5489bb4fa9c3%2F5396b7ee-1abb-403e-9710-6a2ad3160349%2F8xyiftm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Probability and Statistics Practice Problem
On a planet far far away from Earth, the IQ of the ruling species is normally distributed with a mean of 102 and a standard deviation of 18. Suppose one individual is randomly chosen. Let \( X \) = IQ of an individual.
#### Questions:
a. **What is the distribution of \( X \)?**
\( X \sim N(\mu, \sigma^2) \)
\( X \sim N( \_\_\_\_ , \_\_\_\_ ) \)
b. **Find the probability that a randomly selected person's IQ is over 84.**
\(\_\_\_\_\_)
*Round your answer to 4 decimal places.*
c. **A school offers special services for all children in the bottom 6% for IQ scores. What is the highest IQ score a child can have and still receive special services?**
\(\_\_\_\_\_)
*Round your answer to 2 decimal places.*
d. **Find the Interquartile Range (IQR) for IQ scores.**
*Round your answers to 2 decimal places.*
- **Q1:** \(\_\_\_\_\_)
- **Q3:** \(\_\_\_\_\_)
- **IQR:** \(\_\_\_\_\_)
#### Hint:
##### Helpful videos:
- [Find a Probability \[+\]](#)
- [Finding a Value Given a Probability \[+\]](#)
- [Hint \[+\]](#)
---
In case calculations are needed for any of the questions above, make sure to reference appropriate statistical techniques and tables (e.g., Z-tables for standard normal distribution, quartile calculations, etc.).
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