To find the area under the standard normal curve between $z = -1.04$ and $z = 2.76$, we need to calculate the probability $P(-1.04 \leq Z \leq 2.76)$ for a standard normal distribution $Z \sim N(0, 1)$.

1. Find $P(Z \leq 2.76)$:
   Using the standard normal table or a calculator, we get: $P(Z \leq 2.76) \approx 0.9970$

2. Find $P(Z \leq -1.04)$:
   Similarly, using the standard normal table: $P(Z \leq -1.04) \approx 0.1492$

3. Calculate $P(-1.04 \leq Z \leq 2.76)$:
   Subtract $P(Z \leq -1.04)$ from $P(Z \leq 2.76)$: $P(-1.04 \leq Z \leq 2.76) = 0.9970 - 0.1492 = 0.8478$

So, the area under the standard normal curve between $z = -1.04$ and $z = 2.76$ is approximately 0.8478.

Would you like more details on this solution?

Here are some questions for further exploration:

1. How would you find the area under the normal curve between any two arbitrary $z$-values?
2. Why is it useful to use standard normal tables or calculators for these problems?
3. How do we interpret the area under the standard normal curve in real-world applications?
4. How would the area change if we used different $z$-values?
5. What steps would you take to find the area between $z = 0$ and $z = 2.76$?

Tip: For quick calculations, use online tools or statistical software to find areas under the normal curve, especially for non-standard values.