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The question asks for the probability \( P(Z < 2.23) \) from the **standard normal distribution**, where the mean \( \mu = 0 \) and standard deviation \( \sigma = 1 \).

### Step-by-Step Solution:

1. **Locate Z = 2.23** on the **Z-table**, which gives the cumulative probability from \( -\infty \) to 2.23.  
2. From the **Z-table**, the cumulative probability for \( Z = 2.23 \) is:

   \[
   P(Z < 2.23) = 0.9871
   \]

3. **Answer:**  
   Expressing the probability rounded to **4 decimal places**:

   \[
   P(Z < 2.23) = 0.9871
   \]

This means the area to the left of \( Z = 2.23 \) under the standard normal curve is 0.9871.

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### Related Questions:
1. What is the cumulative probability for \( Z < 1.96 \)?
2. How do you interpret probabilities in a standard normal distribution?
3. What is the probability \( P(Z > 2.23) \) using the complement rule?
4. How do we calculate probabilities when Z-scores are negative?
5. What is the total area under the standard normal curve?

**Tip:** When calculating probabilities for normal distributions, if Z-scores aren't integers, a Z-table or software tools (like Excel or calculators) can be very handy.

For a standard normal distribution, find: P(z < 2.23). Express the probability as a decimal rounded to 4 decimal places.

Learn how to find the probability P(z < 2.23) for a standard normal distribution using Z-scores. This detailed solution includes step-by-step guidance for calculating cumulative probabilities and interpreting Z-tables. Suitable for students in Grades 10-12.

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