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Complete the statement. Round your answer to the nearest thousandth.\newlineIn a population that is normally distributed with mean 1919 and standard deviation 1212, the bottom 10%10\% 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 1919 and standard deviation 1212, the bottom 10%10\% of the values are those less than ___.
  1. Find z-score for 1010%: Find the z-score for 10%10\%. Using a z-table or calculator, the z-score for 10%10\% is approximately −1.282-1.282.
  2. Use z-score formula: Use the z-score formula to solve for XX.μ\mu: 1919σ\sigma: 1212ZZ: −1.282-1.282Z=X−μσZ = \frac{X - \mu}{\sigma}−1.282=X−1912-1.282 = \frac{X - 19}{12}
  3. Multiply to isolate XX: Multiply both sides by the standard deviation to isolate (X−μ)(X - \mu).\newline−1.282×12=X−19-1.282 \times 12 = X - 19
  4. Perform the multiplication: Perform the multiplication.\newline−15.384=X−19-15.384 = X - 19
  5. Add mean to solve for X: Add the mean to both sides to solve for X.\newlineX=−15.384+19X = -15.384 + 19
  6. Calculate X value: Calculate the value of X.\newlineX=3.616X = 3.616
  7. Round to nearest thousandth: Round the answer to the nearest thousandth.\newlineX≈3.616X \approx 3.616 (rounded to three decimal places)

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