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The question involves the normal distribution model \( N(100, 16) \), where the mean IQ score (\(\mu\)) is 100, and the standard deviation (\(\sigma\)) is 16.

To find the percentage of people with IQs expected to be between 120 and 136, we can proceed as follows:

1. **Convert 120 and 136 to z-scores** using the formula:

   \[
   z = \frac{x - \mu}{\sigma}
   \]

   - For 120:
     \[
     z = \frac{120 - 100}{16} = \frac{20}{16} = 1.25
     \]

   - For 136:
     \[
     z = \frac{136 - 100}{16} = \frac{36}{16} = 2.25
     \]

2. **Find the corresponding probabilities** for these z-scores from the standard normal distribution table:

   - The probability for \( z = 1.25 \) is approximately \( 0.8944 \).
   - The probability for \( z = 2.25 \) is approximately \( 0.9878 \).

3. **Calculate the difference between these probabilities** to get the probability of an IQ being between 120 and 136:

   \[
   0.9878 - 0.8944 = 0.0934
   \]

4. **Convert to a percentage**:

   \[
   0.0934 \times 100 = 9.3\%
   \]

So, approximately **9.3%** of people’s IQs are expected to be between 120 and 136.

Would you like more details on this calculation or have any questions?

### Related Questions:
1. How would the percentages change if the mean IQ shifted to 110?
2. What percentage of people would have an IQ between 85 and 115?
3. How would we calculate the percentage for an IQ range below the mean, say between 70 and 85?
4. What is the probability of having an IQ greater than 136?
5. How would the results change if the standard deviation was different, say 20 instead of 16?

### Tip:
For any normal distribution problem, converting raw scores to z-scores simplifies the use of standard normal distribution tables to find probabilities.

What percent of people's IQs are expected to be between 120 and 136, given the Normal model N(100,16) describing IQ scores?

Learn to calculate the percentage of IQ scores expected between 120 and 136 using the Normal distribution model N(100,16). This problem demonstrates the use of z-scores and probability concepts, suitable for high school students (Grades 10-12).

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