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Complete the statement. Round your answer to the nearest thousandth.\newlineIn a population that is normally distributed with mean 3636 and standard deviation 1616, the bottom 20%20\% 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 3636 and standard deviation 1616, the bottom 20%20\% of the values are those less than ___.
  1. Find z-score for 2020%: To find the value that corresponds to the bottom 20%20\% of the population, we need to use the z-score table to find the z-score that corresponds to a cumulative probability of 0.200.20.
  2. Lookup z-score in table: Looking up the z-score for a cumulative probability of 0.200.20 in the z-score table, we find that the z-score is approximately −0.84-0.84.
  3. Use z-score formula: Now we use the z-score formula to find the value: X=μ+zσX = \mu + z\sigma, where XX is the value we are looking for, μ\mu is the mean, zz is the z-score, and σ\sigma is the standard deviation.
  4. Plug in values: Plug in the values: X=36+(−0.84)(16)X = 36 + (-0.84)(16).
  5. Calculate value: Calculate the value: X=36−13.44X = 36 - 13.44.
  6. Round to nearest thousandth: X=22.56X = 22.56, but we need to round to the nearest thousandth.
  7. Round to nearest thousandth: X=22.56X = 22.56, but we need to round to the nearest thousandth.Rounded to the nearest thousandth, the value is 22.56022.560.

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