The "z-number" refers to the z-score corresponding to a given cumulative probability in a standard normal distribution. To find the z-scores for the probabilities, you can use a z-table or a statistical calculator. Here are the z-scores for the given probabilities:

(a) $z_{0.4251}$:
For a cumulative probability of 0.4251, the corresponding z-score is approximately -0.19.

(b) $z_{0.4015}$:
For a cumulative probability of 0.4015, the corresponding z-score is approximately -0.25.

(c) $z_{0.3790}$:
For a cumulative probability of 0.3790, the corresponding z-score is approximately -0.31.

(d) $z_{0.4951}$:
For a cumulative probability of 0.4951, the corresponding z-score is approximately -0.01.

Would you like more details on how to interpret the z-table or how these values are calculated?

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Here are five related questions:

1. How can you use a z-table to find probabilities for any given z-score?
2. What is the significance of the standard normal distribution in statistics?
3. How do z-scores help in determining percentiles?
4. How do you calculate z-scores for given values of the mean and standard deviation?
5. How do you find probabilities for z-scores greater than 1.00?

Tip: Always remember that the z-score represents the number of standard deviations a data point is from the mean in a normal distribution.