The normal distribution shown has a mean of 63 and a standard deviation of 8. What percent of the area under the normal curve is represented by the shaded region? Round your answer to the nearest hundredth.  

To determine the percentage of the area under the normal curve represented by the shaded region, we need to know the specific region being shaded (e.g., to the left of a certain value, between two values, or to the right of a certain value). Since the description of the shaded region isn't provided, I'll explain the general approach, and you can provide the missing details.

### General Steps:
1. **Determine the z-score(s):**  
   A z-score represents how many standard deviations a value is away from the mean. The formula to calculate the z-score for a given value \(X\) is:
   \[
   z = \frac{X - \mu}{\sigma}
   \]
   where:
   - \( \mu \) is the mean,
   - \( \sigma \) is the standard deviation.

2. **Use the z-score to find the corresponding probability (area):**
   - The area under the curve corresponds to the cumulative probability.
   - This can be found using z-tables, a calculator, or statistical software.

3. **Calculate the percentage of the area:**
   - The area (probability) is usually given as a decimal, so multiply by 100 to convert it to a percentage.

### Example 1: Shaded area to the left of \(X = 55\)

   - Calculate the z-score for \(X = 55\):
     \[
     z = \frac{55 - 63}{8} = \frac{-8}{8} = -1
     \]
   - The probability corresponding to \(z = -1\) (using a z-table) is approximately 0.1587.
   - So, the area to the left of 55 is 15.87%.

### Example 2: Shaded area between \(X = 55\) and \(X = 71\)

   - Calculate the z-scores for both values:
     \[
     z_{55} = \frac{55 - 63}{8} = -1
     \]
     \[
     z_{71} = \frac{71 - 63}{8} = 1
     \]
   - The cumulative probability for \(z = -1\) is 0.1587 and for \(z = 1\) is 0.8413.
   - The area between \(X = 55\) and \(X = 71\) is \(0.8413 - 0.1587 = 0.6826\).
   - So, the percentage is 68.26%.

Please provide the details of the shaded region, and I can give you the exact percentage for your case.

The normal distribution shown has a mean of 63 and a standard deviation of 8. What percent of the area under the normal curve is represented by the shaded region? Round your answer to the nearest hundredth.

Learn how to calculate the percent area under a normal curve with a mean of 63 and a standard deviation of 8. This guide covers key statistical concepts like the normal distribution, Z-scores, and the Empirical Rule. Suitable for high school students in Grades 10-12.

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