To solve this problem, we need to find the area under the standard normal curve between the z-scores $z = 0.65$ and $z = 1.6$.

1. Find the area to the left of $z = 0.65$: Using a standard normal distribution table or a calculator, we find the cumulative area up to $z = 0.65$.

   • $P(Z \leq 0.65) \approx 0.7422$

2. Find the area to the left of $z = 1.6$: Similarly, we find the cumulative area up to $z = 1.6$.

   • $P(Z \leq 1.6) \approx 0.9452$

3. Calculate the area between $z = 0.65$ and $z = 1.6$: Subtract the area at $z = 0.65$ from the area at $z = 1.6$.

   • $\text{Area} = 0.9452 - 0.7422 = 0.2030$

4. Convert to percentage: Multiply by 100 to get the percentage.

   • $0.2030 \times 100 = 20.3\%$

Rounding to the nearest whole percent, the answer is: $\text{The percent of the total area between } z = 0.65 \text{ and } z = 1.6 \text{ is } 20\%.$

Would you like more details on this calculation or have any questions?

Here are some related questions for further practice:

1. What is the area between $z = -1.5$ and $z = 1.5$ on the standard normal curve?
2. How do we find the area to the right of a given z-score?
3. Why is the standard normal distribution centered around $z = 0$?
4. How would the area change if we extended the range from $z = 0.65$ to $z = 2$?
5. What does a z-score represent in terms of standard deviations from the mean?

Tip: Always verify the z-scores from tables or calculators for accurate cumulative probabilities.