Assume that adults have IQ scores that are normally distributed witha mean of u =100 and a standard deviation a = 15. Find the probability that a randomly selected adult has an IQ less than 115. 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 115 is . (Type an integer or decimal rounded to four decimal places as needed.)

MATLAB: An Introduction with Applications
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Author:Amos Gilat
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**Understanding IQ Probability Distributions**

Assume that adults have IQ scores that are normally distributed with a mean of \( \mu = 100 \) and a standard deviation \( \sigma = 15 \). To find the probability that a randomly selected adult has an IQ less than 115, follow these steps:

1. **Accessing the Necessary Data:**
   - You will need to refer to a standard normal distribution table to find the probabilities. Links are provided:
     - [Click to view page 1 of the table.](#)
     - [Click to view page 2 of the table.](#)

2. **Calculation:**
   - The task requires determining the cumulative probability up to an IQ score of 115.
   - Convert IQ score to a z-score, which is calculated by: 
     \[
     z = \frac{X - \mu}{\sigma}
     \]
     Where \( X \) is the IQ score, \( \mu \) is the mean, and \( \sigma \) is the standard deviation.

3. **Result:**
   - You will input the probability value rounded to four decimal places into the provided field.

**Note:** The exercise explores understanding statistical distributions and the use of z-tables to interpret real-world data.
Transcribed Image Text:**Understanding IQ Probability Distributions** Assume that adults have IQ scores that are normally distributed with a mean of \( \mu = 100 \) and a standard deviation \( \sigma = 15 \). To find the probability that a randomly selected adult has an IQ less than 115, follow these steps: 1. **Accessing the Necessary Data:** - You will need to refer to a standard normal distribution table to find the probabilities. Links are provided: - [Click to view page 1 of the table.](#) - [Click to view page 2 of the table.](#) 2. **Calculation:** - The task requires determining the cumulative probability up to an IQ score of 115. - Convert IQ score to a z-score, which is calculated by: \[ z = \frac{X - \mu}{\sigma} \] Where \( X \) is the IQ score, \( \mu \) is the mean, and \( \sigma \) is the standard deviation. 3. **Result:** - You will input the probability value rounded to four decimal places into the provided field. **Note:** The exercise explores understanding statistical distributions and the use of z-tables to interpret real-world data.
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