Answer :
To find the area under the standard normal distribution curve between two z-scores, we can utilize the Standard Normal Distribution Table, which provides the cumulative probability up to a given z-score. Here are the steps to find the area between z = 0.85 and z = 1.09:
1. **Find the area under the curve to the left of z = 0.85:**
- Look up the cumulative probability for z = 0.85 in the Standard Normal Distribution Table.
- The table entry for z = 0.85 typically gives the area under the curve from the left end up to z = 0.85.
2. **Find the area under the curve to the left of z = 1.09:**
- Similarly, look up the cumulative probability for z = 1.09 in the Standard Normal Distribution Table.
- The table entry for z = 1.09 gives the area under the curve from the left end up to z = 1.09.
3. **Calculate the area between z = 0.85 and z = 1.09:**
- Subtract the area to the left of z = 0.85 from the area to the left of z = 1.09.
- This will give us the area under the curve between the two z-scores.
4. **Round the result to four decimal places:**
- After subtracting, we will round the result to four decimal places as per the requirement.
Using these steps, let us find and calculate the area:
1. **Area to the left of z = 0.85** (from the Standard Normal Distribution Table) is typically around 0.8023.
2. **Area to the left of z = 1.09** (from the Standard Normal Distribution Table) is typically around 0.8621.
3. **Calculate the area between z = 0.85 and z = 1.09:**
- Area between z = 0.85 and z = 1.09 = Area to the left of z = 1.09 - Area to the left of z = 0.85
- Area between z = 0.85 and z = 1.09 = 0.8621 - 0.8023
- Area between z = 0.85 and z = 1.09 = 0.0598
4. **The area is already rounded to four decimal places, so our final answer is:**
- The area between z = 0.85 and z = 1.09 is approximately 0.0598.
