### Probability Calculation of IQ Scores#### Assumptions:Adults have IQ scores that are normally distributed with:- **Mean ($\mu$)**: 100- **Standard Deviation ($\sigma$)**: 20#### Problem:Find the probability that a randomly selected adult has an IQ less than 140.#### Instructions:To solve this problem, follow these steps:1. **Access the Z-table**: The Z-table is used to find the area under the normal curve. - [Click to view page 1 of the table.](#) - [Click to view page 2 of the table.](#)2. **Formula to find Z-score**: \[ Z = \frac{(X - \mu)}{\sigma} \] Where $ X $ is the IQ score of 140.3. **Calculate Z-score**: \[ Z = \frac{(140 - 100)}{20} = 2 \]4. **Look up Z-score in the Z-table**: Find the probability corresponding to $ Z = 2 $ in the Z-table. 5. **Result**: The probability that a randomly selected adult has an IQ less than 140 is $\_\_\_\_$. (Type an integer or decimal rounded to four decimal places as needed.) ---For educational purposes, this problem teaches students how to use the properties of the normal distribution and the Z-table to find probabilities of IQ scores.

Obtain the standard z-score for the random variable equals 140 The standard z-score for the random…

Assume that adults have IQ scores that are normally distributed with a mean of u= 100 and a standard deviation o= 20. Find the probability that a randomly selected adult has an IQ less than 140. 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 140 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 u= 100 and a standard deviation o= 20. Find the probability that a randomly selected adult has an IQ less than 140. 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 140 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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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

Question

### Probability Calculation of IQ Scores

#### Assumptions:
Adults have IQ scores that are normally distributed with:
- **Mean ($\mu$)**: 100
- **Standard Deviation ($\sigma$)**: 20

#### Problem:
Find the probability that a randomly selected adult has an IQ less than 140.

#### Instructions:
To solve this problem, follow these steps:
1. **Access the Z-table**: The Z-table is used to find the area under the normal curve.
- [Click to view page 1 of the table.](#)
- [Click to view page 2 of the table.](#)

2. **Formula to find Z-score**:
\[ Z = \frac{(X - \mu)}{\sigma} \]
Where $ X $ is the IQ score of 140.

3. **Calculate Z-score**:
\[ Z = \frac{(140 - 100)}{20} = 2 \]

4. **Look up Z-score in the Z-table**:
Find the probability corresponding to $ Z = 2 $ in the Z-table.

5. **Result**:
The probability that a randomly selected adult has an IQ less than 140 is $\_\_\_\_$. (Type an integer or decimal rounded to four decimal places as needed.)

---
For educational purposes, this problem teaches students how to use the properties of the normal distribution and the Z-table to find probabilities of IQ scores.

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