It seems you're trying to find specific z-scores using the standard normal (z) table, also known as the Z-table. This table provides the area to the left of a given z-value in a standard normal distribution. Let’s break down the problem and figure out how to solve it for each case:

(a) Find $z_{0.0199}$

Here, we want to find the z-score where the cumulative area (to the left) is 0.0199. This corresponds to the probability or area under the standard normal curve.

1. Check the Z-table for the closest cumulative probability of 0.0199.
2. The Z-table gives us the value of $z$ associated with this cumulative probability.

(b) Find $z_{0.2486}$

We are looking for the z-value where the cumulative area is 0.2486. Again, use the Z-table to find the corresponding z-score.

(c) Find $z_{0.4463}$

In this case, the cumulative area is 0.4463. Using the Z-table, we can find the corresponding z-value.

(d) Find $z_{0.4934}$

For this case, where the cumulative area is 0.4934, we look it up in the Z-table to find the corresponding z-score.

Let me go ahead and find these values for you:

I'll retrieve the accurate values from the standard normal distribution table:

• (a) z₀.₀₁₉₉ corresponds to approximately -2.05.
• (b) z₀.₂₄₈₆ corresponds to approximately -0.65.
• (c) z₀.₄₄₆₃ corresponds to approximately -0.12.
• (d) z₀.₄₉₃₄ corresponds to approximately -0.02.

It looks like your answers are almost correct, but slight rounding issues might be occurring. Double-check the precision you’re using (i.e., two decimal places). The correct answers should be:

Correct Answers:

• (a) -2.05
• (b) -0.65
• (c) -0.12
• (d) -0.02

Let me know if you need more details or help! Would you like me to provide further explanations or examples?

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Related Questions:

1. How can you calculate the z-score from a given probability using the Z-table?
2. What is the relationship between cumulative probability and z-scores in statistics?
3. How do you calculate probabilities using the z-distribution in hypothesis testing?
4. Can the Z-table be used for both one-tailed and two-tailed tests? If so, how?
5. How do you interpret negative z-scores in terms of probability?

Tip: Always ensure you're checking the correct row and column in the Z-table, as small differences in values can lead to slight discrepancies.