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 less than 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 less than 141 is. (Type an integer or decimal rounded to four decimal places as needed.)
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 less than 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 less than 141 is. (Type an integer or decimal rounded to four 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
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Number 16
![**Understanding Probability in Normal Distribution**
In this exercise, we are tasked with finding the probability that a randomly selected adult has an IQ less than 141, given that IQ scores are normally distributed with a mean (μ) of 105 and a standard deviation (σ) of 20.
To solve this problem, you should proceed as follows:
1. **Identify the Parameters:**
- Mean (μ) = 105
- Standard Deviation (σ) = 20
- Target IQ < 141
2. **Standardize the Variable:**
- Use the z-score formula:
\[
z = \frac{X - \mu}{\sigma}
\]
- Substitute X with 141, μ with 105, and σ with 20.
3. **Calculate the Z-score:**
- This will give the number of standard deviations 141 is away from the mean.
4. **Find the Probability:**
- Use a Z-table or statistical software to find the probability corresponding to the calculated Z-score. This value represents the probability that an individual’s IQ is less than 141.
5. **Report the Probability:**
- The probability should be expressed as a decimal rounded to four decimal places.
This exercise illustrates an important application of normal distribution in statistics and provides insight into how probabilities are derived from standardized scores.
Please note, the problem references pages of a table for additional context, indicating that a standard normal distribution table might be useful for finding probabilities.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fffc517a8-8d25-4dba-b5b9-bbe3039266d7%2Fb78f5f09-e59c-4c9f-84a8-84202f701b55%2Fvoej50th_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Understanding Probability in Normal Distribution**
In this exercise, we are tasked with finding the probability that a randomly selected adult has an IQ less than 141, given that IQ scores are normally distributed with a mean (μ) of 105 and a standard deviation (σ) of 20.
To solve this problem, you should proceed as follows:
1. **Identify the Parameters:**
- Mean (μ) = 105
- Standard Deviation (σ) = 20
- Target IQ < 141
2. **Standardize the Variable:**
- Use the z-score formula:
\[
z = \frac{X - \mu}{\sigma}
\]
- Substitute X with 141, μ with 105, and σ with 20.
3. **Calculate the Z-score:**
- This will give the number of standard deviations 141 is away from the mean.
4. **Find the Probability:**
- Use a Z-table or statistical software to find the probability corresponding to the calculated Z-score. This value represents the probability that an individual’s IQ is less than 141.
5. **Report the Probability:**
- The probability should be expressed as a decimal rounded to four decimal places.
This exercise illustrates an important application of normal distribution in statistics and provides insight into how probabilities are derived from standardized scores.
Please note, the problem references pages of a table for additional context, indicating that a standard normal distribution table might be useful for finding probabilities.
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