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.