The z-score above which 10% of a normally distributed population exists, z0.10 , is closest to

To find the z-score above which 10% of a normally distributed population exists, we can follow these steps:

1. Break Down the Problem

We need to find the z-score (let's denote it as $z_{0.10}$) that corresponds to the upper 10% of the standard normal distribution. This means we want to find the z-score such that 90% of the distribution lies below this value.

2. Relevant Concepts

In a standard normal distribution:

• The total area under the curve is 1.
• The area to the left of $z_{0.10}$ is 0.90 since we are looking for the z-score above which 10% lies.

3. Analysis and Detail

Using the standard normal distribution table (Z-table) or a calculator, we can find the z-score corresponding to an area of 0.90.

1. Look up 0.90 in the Z-table, which represents the cumulative area.
2. The z-score that corresponds to an area of 0.90 is typically around 1.28.

4. Verify and Summarize

To verify, we can use statistical software or a calculator to confirm that the z-score corresponding to the cumulative probability of 0.90 is indeed 1.28.

Final Answer

The z-score $z_{0.10}$ above which 10% of the normally distributed population exists is approximately 1.28.