Assume that adults have IQ scores that are normally distributed with a mean of µ= 105 and a standard deviation a=20. Find the probability that a randomly selected adult has an IQ between 87 and 123. Click to view page 1 of the table. Click to view page 2 of the table. The probability that a randomly selected adult has an IQ between 87 and 123 is (Type an integer or decimal rounded to four decimal places as needed.) CDD
Assume that adults have IQ scores that are normally distributed with a mean of µ= 105 and a standard deviation a=20. Find the probability that a randomly selected adult has an IQ between 87 and 123. Click to view page 1 of the table. Click to view page 2 of the table. The probability that a randomly selected adult has an IQ between 87 and 123 is (Type an integer or decimal rounded to four decimal places as needed.) CDD
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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Question 17
![**IQ Probability Calculation**
Assume that adults have IQ scores that are normally distributed with a mean (\( \mu \)) of 105 and a standard deviation (\( \sigma \)) of 20.
**Task:**
Find the probability that a randomly selected adult has an IQ between 87 and 123.
**Instructions:**
- Refer to page 1 and page 2 of the table for necessary values.
- Enter the probability as an integer or a decimal rounded to four decimal places as needed.
---
**Calculate the Probability:**
1. Determine the z-scores for the IQ values of 87 and 123 using the formula:
\[
z = \frac{(X - \mu)}{\sigma}
\]
where \( X \) is the IQ score.
2. Convert the z-scores to probabilities using the standard normal distribution table.
3. Subtract the probability of IQ 87 from the probability of IQ 123 to get the final probability.
Submit the calculated probability in the provided box.
**Navigation:**
Click "Next" to proceed once you have entered your answer.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fffc517a8-8d25-4dba-b5b9-bbe3039266d7%2F546e21c5-cf96-4cd3-99d3-02498469ef5e%2Fiw0dvji_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**IQ Probability Calculation**
Assume that adults have IQ scores that are normally distributed with a mean (\( \mu \)) of 105 and a standard deviation (\( \sigma \)) of 20.
**Task:**
Find the probability that a randomly selected adult has an IQ between 87 and 123.
**Instructions:**
- Refer to page 1 and page 2 of the table for necessary values.
- Enter the probability as an integer or a decimal rounded to four decimal places as needed.
---
**Calculate the Probability:**
1. Determine the z-scores for the IQ values of 87 and 123 using the formula:
\[
z = \frac{(X - \mu)}{\sigma}
\]
where \( X \) is the IQ score.
2. Convert the z-scores to probabilities using the standard normal distribution table.
3. Subtract the probability of IQ 87 from the probability of IQ 123 to get the final probability.
Submit the calculated probability in the provided box.
**Navigation:**
Click "Next" to proceed once you have entered your answer.
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