The question asks for the area under the shaded region of the standard normal distribution between $z = -1.77$ and $z = 2.36$. Since this is a standard normal distribution with mean $0$ and standard deviation $1$, we can use a standard normal table (z-table) or a calculator to determine the cumulative probabilities at these $z$-values.

Step 1: Find the cumulative probabilities

From a standard normal table:

1. For $z = -1.77$:
   The cumulative probability (area to the left of $z = -1.77$) is approximately 0.0384.

2. For $z = 2.36$:
   The cumulative probability (area to the left of $z = 2.36$) is approximately 0.9909.

Step 2: Compute the area between $z = -1.77$ and $z = 2.36$

The area between these two points is calculated as: $\text{Area} = P(z \leq 2.36) - P(z \leq -1.77)$ Substitute the values: $\text{Area} = 0.9909 - 0.0384 = 0.9525$

Final Answer:

The area under the shaded region is approximately 0.9525 or 95.25%.

Do you need further clarification or additional details?

Here are some follow-up questions to expand on this:

1. How do you interpret the area under the standard normal curve?
2. How is the z-score calculated for a given value in any normal distribution?
3. What does it mean if a z-score is negative?
4. How would you calculate the area for non-standard normal distributions?
5. How can you use technology (e.g., Excel, calculators) to find areas under the normal curve?

Tip: The z-table only gives cumulative probabilities (left areas), so to find areas between two $z$-values, subtract the smaller cumulative area from the larger one.