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Complete the statement. Round your answer to the nearest thousandth.\newlineIn a population that is normally distributed with mean 3838 and standard deviation 99, 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 3838 and standard deviation 99, the bottom 10%10\% of the values are those less than ___.
  1. Find z-score for bottom 10%10\%: We need to find the z-score that corresponds to the bottom 10%10\% of a normal distribution.
  2. Use z-table to determine z-score: Using a z-table, we find that the z-score for the bottom 10%10\% is approximately −1.28-1.28.
  3. Apply 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 that is less than the bottom 10%10\%.
  4. Solve for X: Rearrange the formula to solve for X: X=z×standard deviation+meanX = z \times \text{standard deviation} + \text{mean}.
  5. Rearrange formula for X: Plug in the values: X=−1.28×9+38X = -1.28 \times 9 + 38.
  6. Substitute values into formula: Calculate the value: X=−11.52+38X = -11.52 + 38.
  7. Calculate XX: X=26.48X = 26.48.
  8. Round to nearest thousandth: Round the answer to the nearest thousandth: X≈26.480X \approx 26.480.

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