What percentage of the normal curve falls between the two Z scores of (Z = –1.61) and (Z = +1.08)?


To determine what percentage of the normal curve falls between the two Z-scores (Z = -1.61 and Z = +1.08), we need to use the standard normal distribution table or a calculator to find the corresponding area under the curve for each Z-score.

### Step 1: Find the area to the left of each Z-score.

1. **Z = -1.61**:
   From the standard normal table, the cumulative probability (area to the left) for Z = -1.61 is approximately **0.0537**.

2. **Z = +1.08**:
   From the standard normal table, the cumulative probability for Z = +1.08 is approximately **0.8599**.

### Step 2: Subtract the two areas.
To find the area between Z = -1.61 and Z = +1.08, subtract the area to the left of Z = -1.61 from the area to the left of Z = +1.08:

\[
0.8599 - 0.0537 = 0.8062
\]

### Step 3: Convert to percentage.
Multiply by 100 to get the percentage:

\[
0.8062 \times 100 = 80.62\%
\]

### Conclusion:
Approximately **80.62%** of the normal curve falls between Z = -1.61 and Z = +1.08.

Would you like further details or have any questions?

Here are 5 related questions:
1. What is the probability outside the range of Z = -1.61 and Z = +1.08?
2. How do you calculate Z-scores from raw data?
3. What is the area under the normal curve for Z = 0?
4. How does the standard deviation affect the shape of the normal curve?
5. How can you use Z-scores to identify outliers?

**Tip**: The area under the entire normal curve always equals 1 (or 100%), which helps verify your calculations.

What percentage of the normal curve falls between the two Z scores of (Z = –1.61) and (Z = +1.08)?

Find out what percentage of the normal curve falls between the Z-scores of -1.61 and +1.08. This solution involves key statistical concepts like Z-scores, standard normal distribution, and cumulative probabilities, and is suitable for high school students studying advanced statistics.

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