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Complete the statement. Round your answer to the nearest thousandth.\newlineIn a population that is normally distributed with mean 2828 and standard deviation 2020, the bottom 10%10\% of the values are those less than ___.

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Q. Complete the statement. Round your answer to the nearest thousandth.\newlineIn a population that is normally distributed with mean 2828 and standard deviation 2020, the bottom 10%10\% of the values are those less than ___.
  1. Find Z-Score: We need to find the z-score that corresponds to the bottom 10%10\% of a normal distribution.
  2. Use Z-Table: Using a z-table, we find that the z-score for the bottom 10%10\% is approximately −1.282-1.282.
  3. Z-Score Formula: Now we use the z-score formula: z=X−meanstandard deviationz = \frac{X - \text{mean}}{\text{standard deviation}}. We need to solve for XX, which represents the value we're looking for.
  4. Rearrange Formula: Rearrange the formula to solve for XX: X=z×standard deviation+meanX = z \times \text{standard deviation} + \text{mean}.
  5. Plug in Values: Plug in the values: X=−1.282×20+28X = -1.282 \times 20 + 28.
  6. Calculate Value: Calculate the value: X=−25.64+28X = -25.64 + 28.
  7. Round to Nearest Thousandth: X=2.36X = 2.36, but we need to round to the nearest thousandth.

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