IQ scores are normally distributed with a mean of 100 and a standard deviation of 15 . Using the empirical rule, determine the interval that would represent the middle $$ 68 \% $$ of IQ scores. Answer Attempt 1 out of 2

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To determine the interval that represents the middle **68%** of IQ scores using the **Empirical Rule**, follow these steps:

### **Empirical Rule Overview**
The Empirical Rule states that for a **normally distributed** dataset:
- **68%** of the data falls within **±1 standard deviation** from the mean.
- **95%** of the data falls within **±2 standard deviations** from the mean.
- **99.7%** of the data falls within **±3 standard deviations** from the mean.

### **Given:**
- **Mean (μ)** = 100
- **Standard Deviation (σ)** = 15

### **Calculating the Interval for 68%:**
Since 68% of the IQ scores lie within **±1 standard deviation** from the mean:

1. **Lower Bound:**
   $$
   \mu - \sigma = 100 - 15 = 85
   $$

2. **Upper Bound:**
   $$
   \mu + \sigma = 100 + 15 = 115
   $$

### **Result:**
The middle **68%** of IQ scores are **between 85 and 115**.

$$
\boxed{85 \leq \text{IQ} \leq 115}
$$
The middle 68% of IQ scores range from 85 to 115.

IQ scores are normally distributed with a mean of 100 and a standard deviation of 15 . Using the empirical rule, determine the interval that would represent the middle \( 68 \% \) of IQ scores. Answer Attempt 1 out of 2

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