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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 1919, the bottom 20%20\% 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 1919, the bottom 20%20\% of the values are those less than ___.
  1. Find z-score for 2020\%: Find the z-score for 2020\%. Using a z-table or calculator, the z-score for 2020\% is approximately −0.842-0.842.
  2. Use z-score formula: Use the z-score formula to solve for XX.
    mean (μ\mu): 1919
    standard deviation (σ\sigma): 1919
    z-score (ZZ): −0.842-0.842
    Z=X−μσZ = \frac{X - \mu}{\sigma}
    −0.842=X−1919-0.842 = \frac{X - 19}{19}
  3. Multiply to isolate XX: Multiply both sides by the standard deviation to isolate X−μX - \mu.−0.842×19=X−19-0.842 \times 19 = X - 19−16.0=X−19-16.0 = X - 19

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