Use the body table to find the specified z-number. (Round the answer to two decimal places.)
(a) z0.4279 =

(b) z0.3997 =

(c) z0.3790 =

(d) z0.4951 =

To find the z-scores that correspond to the given cumulative probabilities (from a standard normal distribution table or z-table), we search for the closest probability values in the body of the table. The z-table provides cumulative probabilities for z-values from the mean (0) to a given z-score.

Let's solve each:

### (a) \( z_{0.4279} \)
- Look for the closest cumulative probability to 0.4279 in the z-table.
- The closest value to 0.4279 is 0.42785, corresponding to \( z = 0.08 \).

Thus, \( z_{0.4279} = 0.08 \).

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### (b) \( z_{0.3997} \)
- Look for the closest cumulative probability to 0.3997.
- The closest value to 0.3997 is 0.39970, corresponding to \( z = 0.25 \).

Thus, \( z_{0.3997} = 0.25 \).

---

### (c) \( z_{0.3790} \)
- Look for the closest cumulative probability to 0.3790.
- The closest value to 0.3790 is 0.37898, corresponding to \( z = 0.31 \).

Thus, \( z_{0.3790} = 0.31 \).

---

### (d) \( z_{0.4951} \)
- Look for the closest cumulative probability to 0.4951.
- The closest value to 0.4951 is 0.49507, corresponding to \( z = 0.01 \).

Thus, \( z_{0.4951} = 0.01 \).

### Summary of z-scores:
- \( z_{0.4279} = 0.08 \)
- \( z_{0.3997} = 0.25 \)
- \( z_{0.3790} = 0.31 \)
- \( z_{0.4951} = 0.01 \)

Would you like further details on any of the steps?

### Relative questions:
1. How do you interpret a z-score in a normal distribution?
2. Can you explain the process of finding a z-score using a z-table?
3. What is the significance of cumulative probability in a normal distribution?
4. How does the z-score relate to standard deviations in a normal distribution?
5. Can you find the probability for a z-score of 0.5 using the z-table?

**Tip:** When using a z-table, round the probability to the nearest value to match the closest cumulative probability in the table.

Use the body table to find the specified z-number. (Round the answer to two decimal places.) (a) z0.4279 = (b) z0.3997 = (c) z0.3790 = (d) z0.4951 =

Learn how to find z-scores corresponding to cumulative probabilities (z0.4279, z0.3997, z0.3790, z0.4951) using the z-table. This problem covers key statistical concepts, including the standard normal distribution and cumulative probability. Suitable for students in Grades 10-12.

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