To find the percent of the total area under the standard normal curve between the z-scores $z = -1.5$ and $z = -0.75$, we need to use the standard normal table provided in the image.

Here’s the step-by-step process:

1. Find the area for $z = -1.5$:

   • The table shows positive z-scores, but because the normal distribution is symmetric, the area for $z = -1.5$ is the same as the area for $z = 1.5$.
   • From the table, for $z = 1.5$, the area is approximately 0.433.

2. Find the area for $z = -0.75$:

   • Similarly, the area for $z = -0.75$ is the same as for $z = 0.75$.
   • From the table, for $z = 0.75$, the area is approximately 0.273.

3. Calculate the difference:

   • The area between $z = -1.5$ and $z = -0.75$ is $0.433 - 0.273 = 0.160$.

4. Convert to percentage:

   • $0.160 \times 100 = 16\%$.

Therefore, the percent of the total area under the curve between $z = -1.5$ and $z = -0.75$ is approximately 16%.

Would you like a deeper explanation or have any other questions?

Related Questions:

1. What is the significance of a z-score in statistics?
2. How would you find the area under the curve for a range of positive z-scores?
3. How can the standard normal distribution be applied in real-world scenarios?
4. What would be the area between z-scores of -2 and 0?
5. How do you use a z-score table to find probabilities for non-standard normal distributions?

Tip:

Remember that the normal distribution table is symmetrical around zero, allowing you to find areas for negative z-scores by looking up their positive counterparts.