decimal places as needed.)
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
Assume that adults have IQ score that are
the probability that a randomly selected adult from this group has an IQ greater than 130.7
![**Question:**
Assume that adults have IQ scores that are normally distributed with a mean of 100.4 and a standard deviation of 19.1. Find the probability that a randomly selected adult has an IQ greater than 130.7. (Hint: Draw a graph.)
**Solution:**
To find the probability that a randomly selected adult from this group has an IQ greater than 130.7:
1. **Calculate the Z-score:**
\[
Z = \frac{X - \mu}{\sigma} = \frac{130.7 - 100.4}{19.1}
\]
where \( X \) is the IQ score of interest, \( \mu \) is the mean IQ score, and \( \sigma \) is the standard deviation.
2. **Use Z-table or calculator:**
Once the Z-score is calculated, use a standard normal distribution table (Z-table) or a calculator to find the probability associated with that Z-score. This probability represents the percentage of the population with IQ scores less than 130.7. Subtract this probability from 1 to find the probability of having an IQ greater than 130.7.
3. **Round the result:**
Round the final probability to four decimal places as needed.
**Graph Explanation:**
You can illustrate this problem with a normal distribution curve:
- **Mean (100.4):** Mark the center of the curve.
- **Standard Deviation (19.1):** Define the width of the curve.
- **Area of Interest (IQ > 130.7):** Shade the area to the right of 130.7 to depict the probability you're trying to find.
**Answer Entry:**
- Once calculated, enter your answer in the answer box and click "Check Answer."
This process will guide users through solving similar statistical problems involving normal distributions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8732b77c-7565-4c55-8f8b-38036d02811d%2Fc62a466f-43f4-4bae-8f2b-9a73994890e9%2Fnmkq4l_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question:**
Assume that adults have IQ scores that are normally distributed with a mean of 100.4 and a standard deviation of 19.1. Find the probability that a randomly selected adult has an IQ greater than 130.7. (Hint: Draw a graph.)
**Solution:**
To find the probability that a randomly selected adult from this group has an IQ greater than 130.7:
1. **Calculate the Z-score:**
\[
Z = \frac{X - \mu}{\sigma} = \frac{130.7 - 100.4}{19.1}
\]
where \( X \) is the IQ score of interest, \( \mu \) is the mean IQ score, and \( \sigma \) is the standard deviation.
2. **Use Z-table or calculator:**
Once the Z-score is calculated, use a standard normal distribution table (Z-table) or a calculator to find the probability associated with that Z-score. This probability represents the percentage of the population with IQ scores less than 130.7. Subtract this probability from 1 to find the probability of having an IQ greater than 130.7.
3. **Round the result:**
Round the final probability to four decimal places as needed.
**Graph Explanation:**
You can illustrate this problem with a normal distribution curve:
- **Mean (100.4):** Mark the center of the curve.
- **Standard Deviation (19.1):** Define the width of the curve.
- **Area of Interest (IQ > 130.7):** Shade the area to the right of 130.7 to depict the probability you're trying to find.
**Answer Entry:**
- Once calculated, enter your answer in the answer box and click "Check Answer."
This process will guide users through solving similar statistical problems involving normal distributions.
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