What Z-Score equates to the 33rd percentile?

To find the Z-score corresponding to the 33rd percentile, we use the fact that Z-scores are based on the standard normal distribution, which is symmetric about the mean of 0 with a standard deviation of 1.

1. The percentile (33rd percentile) represents the probability, so we want to find the Z-score such that 33% of the distribution falls to the left of it. In statistical terms, we need to find \( Z \) such that \( P(Z < z) = 0.33 \).
  
2. Using standard normal distribution tables or a calculator, the Z-score corresponding to the 33rd percentile is approximately:

\[
Z \approx -0.44
\]

So, the Z-score that equates to the 33rd percentile is approximately \( -0.44 \).

Would you like more details on how to use Z-tables or a step-by-step explanation of this? Let me know if you have any questions!

Here are five related questions:
1. How do you calculate the Z-score for a specific data point?
2. What is the Z-score for the 50th percentile?
3. How do you interpret Z-scores in the context of normal distributions?
4. How is the percentile rank related to the cumulative probability?
5. How

Discover how to find the Z-score corresponding to the 33rd percentile in a standard normal distribution. This solution explains the concept of Z-scores, percentiles, and their relationship with the standard normal distribution. Suitable for students in Grades 10-12.

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