Find the area, to the nearest thousandth, of the standard normal distribution between the given z-scores.
z = 1.12 and z = 1.73

To find the area under the standard normal distribution between the z-scores \( z = 1.12 \) and \( z = 1.73 \), we need to find the probabilities corresponding to these z-scores and then calculate the difference.

### Step 1: Find the area to the left of \( z = 1.73 \).
Using the standard normal distribution table, or a calculator, we get:
\[
P(z \leq 1.73) \approx 0.9582
\]

### Step 2: Find the area to the left of \( z = 1.12 \).
Similarly, we find:
\[
P(z \leq 1.12) \approx 0.8686
\]

### Step 3: Calculate the area between \( z = 1.12 \) and \( z = 1.73 \).
Subtract the area to the left of \( z = 1.12 \) from the area to the left of \( z = 1.73 \):
\[
0.9582 - 0.8686 = 0.0896
\]

Thus, the area under the standard normal distribution curve between \( z = 1.12 \) and \( z = 1.73 \) is approximately **0.090** (to the nearest thousandth).

Would you like more details on how to read the z-table or have any questions?

### Related Questions:
1. What is the area under the standard normal curve between \( z = -1.5 \) and \( z = 2.0 \)?
2. How do you interpret the area under the standard normal curve?
3. What is the probability of a z-score falling between two values in the standard normal distribution?
4. How can you calculate the area between two z-scores using a calculator?
5. What is the area outside \( z = -1.12 \) and \( z = 1.12 \)?

### Tip:
When using the z-table, always ensure whether it provides the area from the left tail or from the mean, as different tables may use different conventions.

Find the area, to the nearest thousandth, of the standard normal distribution between the given z-scores. z = 1.12 and z = 1.73

Find the area under the standard normal distribution curve between z-scores 1.12 and 1.73, with a detailed step-by-step solution. Learn about key statistical concepts such as z-scores, probability, and the normal distribution. This problem is ideal for students in Grades 10-12.

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