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

Question

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

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Solution

To find the z-score above which 10% of a normally distributed population exists, we need to determine the z-score corresponding to the 90th percentile (since 100% - 10% = 90%).

  1. Identify the cumulative probability: We need the z-score for which the cumulative probability is 0.90.

  2. Use the standard normal distribution table or a calculator: Look up the cumulative probability of 0.90 in the z-table or use a statistical calculator to find the corresponding z-score.

  3. Find the z-score: The z-score corresponding to the 90th percentile is approximately 1.28.

Therefore, the z-score above which 10% of a normally distributed population exists, z0.10 z_{0.10} , is closest to 1.28.

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