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Complete the statement. Round your answer to the nearest thousandth.\newlineIn a population that is normally distributed with mean 11 and standard deviation 2121, the bottom 30%30\% of the values are those less than ___.

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Full solution

Q. Complete the statement. Round your answer to the nearest thousandth.\newlineIn a population that is normally distributed with mean 11 and standard deviation 2121, the bottom 30%30\% of the values are those less than ___.
  1. Find z-score for 3030th percentile: Find the z-score for the 3030th percentile. Using a z-table or calculator, the z-score for 30%30\% is approximately −0.52-0.52.
  2. Use z-score formula: Use the z-score formula to find the value (X)(X).Z=(X−mean)standard deviationZ = \frac{(X - \text{mean})}{\text{standard deviation}}−0.52=(X−1)21-0.52 = \frac{(X - 1)}{21}
  3. Solve for X: Solve for X.\newlineX−1=−0.52×21X - 1 = -0.52 \times 21\newlineX−1=−10.92X - 1 = -10.92\newlineX=−10.92+1X = -10.92 + 1\newlineX=−9.92X = -9.92

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