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Complete the statement. Round your answer to the nearest thousandth.\newlineIn a population that is normally distributed with mean 4848 and standard deviation 1919, the bottom 30%30\% 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 4848 and standard deviation 1919, the bottom 30%30\% of the values are those less than ___.
  1. Find z-score for 3030%: We need to find the z-score that corresponds to the bottom 30%30\% of the normal distribution.
  2. Use z-table for −0.52-0.52: Using a z-table, we find that the z-score for the bottom 30%30\% is approximately −0.52-0.52.
  3. Apply z-score formula: Now we use the z-score formula: z=X−meanstandard deviationz = \frac{X - \text{mean}}{\text{standard deviation}}, where XX is the value we are looking for.
  4. Rearrange formula for XX: We 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=−0.52×19+48X = -0.52 \times 19 + 48.
  6. Calculate X: Calculate the value of XX: X=−9.88+48X = -9.88 + 48.
  7. Round to nearest thousandth: X=38.12X = 38.12, but we need to round to the nearest thousandth.
  8. Final answer: The final answer, rounded to the nearest thousandth, is 38.12038.120.

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