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Complete the statement. Round your answer to the nearest thousandth.\newlineIn a population that is normally distributed with mean 3434 and standard deviation 66, the bottom 70%70\% 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 3434 and standard deviation 66, the bottom 70%70\% of the values are those less than ___.
  1. Find z-score for 7070\%: Find the z-score for 70%70\%.\newlineUsing a z-table or calculator, the z-score for 70%70\% is approximately 0.5240.524.
  2. Use z-score formula: Use the z-score formula to solve for XX.
    mean (μ\mu): 3434
    standard deviation (σ\sigma): 66
    z-score (ZZ): 0.5240.524
    Z=X−μσZ = \frac{X - \mu}{\sigma}
    0.524=X−3460.524 = \frac{X - 34}{6}
  3. Multiply to isolate XX: Multiply both sides by the standard deviation to isolate (X−μ)(X - \mu).0.524×6=X−340.524 \times 6 = X - 343.144=X−343.144 = X - 34
  4. Add mean to solve: Add the mean to both sides to solve for XX.X=3.144+34X = 3.144 + 34X=37.144X = 37.144
  5. Round the answer: Round the answer to the nearest thousandth. X≈37.144X \approx 37.144

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