Use the body table to find the specified z-number. (Enter your answers to two decimal places.)
(a)    z0.4251


(b)    z0.4015


(c)    z0.3790


(d)    z0.4951

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.

Use the body table to find the specified z-number. (Enter your answers to two decimal places.)
(a) z0.4251
(b) z0.4015
(c) z0.3790
(d) z0.4951

Learn how to find z-scores for given cumulative probabilities such as z0.4251, z0.4015, z0.3790, and z0.4951 using a standard normal distribution table (Z-table). This example is perfect for students in Grades 10-12 learning about statistics and the normal distribution.

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