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The problem asks to find the area under the standard normal curve between \( z = -2.97 \) and \( z = -2.67 \). This requires finding the cumulative probabilities associated with these \( z \)-scores and then subtracting them to find the area in between.

We can do this by looking up these \( z \)-scores in the standard normal table (Z-table) or using a calculator that can compute the cumulative distribution function (CDF) for a standard normal distribution.

1. Look up the cumulative probability for \( z = -2.97 \) in the Z-table.  
   - This value is approximately \( 0.0015 \).

2. Look up the cumulative probability for \( z = -2.67 \) in the Z-table.  
   - This value is approximately \( 0.0038 \).

3. To find the area between these two values, subtract the smaller cumulative probability from the larger one:
   \[
   \text{Area} = 0.0038 - 0.0015 = 0.0023
   \]

Thus, the area under the standard normal curve between \( z = -2.97 \) and \( z = -2.67 \) is approximately **0.0023**.

Would you like more details on how to interpret Z-tables or use a calculator for this process? 

Here are five follow-up questions related to this problem:
1. How do you find cumulative probabilities for positive \( z \)-scores?
2. What is the total area under the standard normal curve?
3. How can you use symmetry of the normal distribution when dealing with negative \( z \)-scores?
4. What is the significance of the area under the curve in probability and statistics?
5. How would you solve this problem using a graphing calculator or software like Excel?

**Tip:** When using Z-tables, remember that the values provided are cumulative probabilities from the far left of the curve up to the given \( z \)-score.

Find the area under the standard normal curve between z = -2.97 and z = -2.67. Round your answer to four decimal places, if necessary.

Learn how to calculate the area under the standard normal curve between z = -2.97 and z = -2.67 using Z-tables or a cumulative distribution function (CDF). This example explains how to subtract cumulative probabilities to find the exact area.

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