Find the area of the shaded region for each standard normal curve.
left parenthesis a right parenthesis(a)
-1.03
0.48

x y graph
left parenthesis b right parenthesis(b)
-1.69
1.69

x y graph
left parenthesis c right parenthesis(c)
-1.73
1.73

x y graph

To find the area of the shaded region under a standard normal curve, we need to find the probability (or area) between the given \( z \)-scores, as the standard normal curve is symmetric around \( z = 0 \) with a total area of 1. We use a standard normal table or a calculator to find the cumulative area corresponding to the \( z \)-scores.

### (a) Between \( z = -1.03 \) and \( z = 0.48 \)
1. Find the cumulative area from the standard normal table for both \( z \)-scores:
   - \( z = -1.03 \) gives a cumulative area of approximately **0.1515**.
   - \( z = 0.48 \) gives a cumulative area of approximately **0.6844**.

2. The area between these two \( z \)-scores is the difference:
   \[
   \text{Area} = 0.6844 - 0.1515 = 0.5329
   \]
   So, the area of the shaded region is **0.5329**.

### (b) Between \( z = -1.69 \) and \( z = 1.69 \)
1. Find the cumulative area from the standard normal table for both \( z \)-scores:
   - \( z = -1.69 \) gives a cumulative area of approximately **0.0455**.
   - \( z = 1.69 \) gives a cumulative area of approximately **0.9545**.

2. The area between these two \( z \)-scores is the difference:
   \[
   \text{Area} = 0.9545 - 0.0455 = 0.9090
   \]
   So, the area of the shaded region is **0.9090**.

### (c) Between \( z = -1.73 \) and \( z = 1.73 \)
1. Find the cumulative area from the standard normal table for both \( z \)-scores:
   - \( z = -1.73 \) gives a cumulative area of approximately **0.0418**.
   - \( z = 1.73 \) gives a cumulative area of approximately **0.9582**.

2. The area between these two \( z \)-scores is the difference:
   \[
   \text{Area} = 0.9582 - 0.0418 = 0.9164
   \]
   So, the area of the shaded region is **0.9164**.

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Do you need any more details or have any questions? 

Here are 5 related questions:
1. How can you find the area of a standard normal curve using a calculator?
2. What is the total area under the standard normal curve?
3. What is the significance of the cumulative area in a standard normal distribution?
4. How do you interpret the area between two \( z \)-scores in a real-world context?
5. How would you compute the area for more extreme \( z \)-scores?

**Tip:** Always remember that the total area under the standard normal curve is 1, and it is symmetric around 0.

Find the area of the shaded region for each standard normal curve: (a) between z = -1.03 and z = 0.48, (b) between z = -1.69 and z = 1.69, (c) between z = -1.73 and z = 1.73.

Learn how to calculate the area of the shaded region between two z-scores under the standard normal curve using cumulative areas. Step-by-step examples include areas between z = -1.03 and z = 0.48, z = -1.69 and z = 1.69, and z = -1.73 and z = 1.73.

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