Find the z-number associated with a 80% level of confidence. (Round the answer to two decimal places.)
z =

To find the z-score associated with an 80% confidence level, we need to find the z-value where 80% of the data lies between -z and +z under the normal distribution curve.

The 80% confidence level implies that 40% of the data lies to the left of -z and 40% lies to the right of +z, leaving 20% outside of the range (10% in each tail).

Thus, we need to find the z-score that corresponds to the cumulative probability of 0.9 (since 0.9 = 0.5 + 0.4). Using standard normal distribution tables or a calculator, the z-value for 0.9 is approximately:

\[
z \approx 1.28
\]

So, the z-value for an 80% confidence level is \( z = 1.28 \).

Do you need further explanation or details?

Here are five related questions for further exploration:
1. How do you calculate the z-value for a 90% confidence level?
2. What is the confidence interval formula in statistics?
3. How is the z-score used in hypothesis testing?
4. How can confidence levels affect sample sizes in statistics?
5. What are the differences between z-scores and t-scores in statistics?

**Tip:** Z-scores provide a way to quantify how many standard deviations a data point is from the mean in a normal distribution.

Find the z-number associated with a 80% level of confidence. (Round the answer to two decimal places.) z =

Learn how to find the z-score associated with an 80% confidence level. This guide covers key statistical concepts like normal distribution and confidence intervals, using standard normal tables to find a z-value of approximately 1.28. Suitable for high school and college-level students.

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