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Complete the statement. Round your answer to the nearest thousandth.\newlineIn a population that is normally distributed with mean 9898 and standard deviation 1313, the bottom 90%90\% 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 9898 and standard deviation 1313, the bottom 90%90\% of the values are those less than ___.
  1. Find z-score: We need to find the z-score that corresponds to the bottom 90%90\% of a normal distribution.
  2. Use z-table: Using a z-table, we find that the z-score for the bottom 90%90\% is approximately 1.281.28.
  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 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=1.28×13+98X = 1.28 \times 13 + 98.
  6. Calculate X: Calculate the value of X: X=16.64+98X = 16.64 + 98.
  7. Correct z-score: X=114.64X = 114.64, but we made a mistake, the z-score for the bottom 90%90\% is not 1.281.28, it's actually −1.28-1.28 because we are looking for the value below the mean, not above it.

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