Use the body table to find the specified z-number. (Round the answer to two decimal places.)
(a) z0.4236 =

Incorrect: Your answer is incorrect.

(b) z0.3997 =

Incorrect: Your answer is incorrect.

(c) z0.3790 =

Incorrect: Your answer is incorrect.

(d) z0.4946 =

To find the z-scores corresponding to the given cumulative probabilities \( P(Z \leq z) \), you typically use the standard normal distribution table (z-table) or a calculator. Let's calculate each one:

### (a) \( z_{0.4236} \)
For \( P(Z \leq z) = 0.4236 \), we need to find the z-value that corresponds to a cumulative probability of 0.4236.

Looking at the z-table, this value is approximately:
- \( z = -0.19 \)

### (b) \( z_{0.3997} \)
For \( P(Z \leq z) = 0.3997 \), check the z-table for this cumulative probability.

The corresponding z-value is approximately:
- \( z = -0.25 \)

### (c) \( z_{0.3790} \)
For \( P(Z \leq z) = 0.3790 \), look up the closest cumulative probability in the z-table.

The corresponding z-value is approximately:
- \( z = -0.31 \)

### (d) \( z_{0.4946} \)
For \( P(Z \leq z) = 0.4946 \), find the cumulative probability.

The corresponding z-value is approximately:
- \( z = -0.01 \)

Would you like more details or have any questions about the z-table process? Here are 5 related questions for deeper exploration:

1. How do you interpret a z-score in statistics?
2. What is the relation between the z-score and cumulative probability?
3. How would you calculate a z-score without a z-table?
4. What is the significance of a negative z-score?
5. How can z-scores be used in hypothesis testing?

**Tip:** When using a z-table, always verify whether you're reading from a standard normal cumulative table (for \( P(Z \leq z) \)) or the tail probability table.

Use the body table to find the specified z-number. (Round the answer to two decimal places.) (a) z0.4236 = Incorrect: Your answer is incorrect. (b) z0.3997 = Incorrect: Your answer is incorrect. (c) z0.3790 = Incorrect: Your answer is incorrect. (d) z0.4946 =

Discover how to find z-scores corresponding to specific cumulative probabilities using the standard normal distribution table. This problem explores z-scores for probabilities such as P(Z ≤ 0.4236), P(Z ≤ 0.3997), P(Z ≤ 0.3790), and P(Z ≤ 0.4946). Learn how to use the z-table for accurate calculations, suitable for high school and introductory college-level statistics.

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