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Complete the statement. Round your answer to the nearest thousandth.\newlineIn a population that is normally distributed with mean 5353 and standard deviation 1010, 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 5353 and standard deviation 1010, the bottom 20%20\% of the values are those less than ___.
  1. Find z-score for bottom 20%20\%: First, we need to find the z-score that corresponds to the bottom 20%20\% of a normal distribution.
  2. Use z-table for z-score: Using a z-table, we find that the z-score for the bottom 20%20\% is approximately −0.842-0.842.
  3. Apply z-score formula: Now we use the z-score formula: z=X−meanstandard deviationz = \frac{X - \text{mean}}{\text{standard deviation}}, where XX is the value we are looking for.
  4. Rearrange formula for XX: We rearrange the formula to solve for XX: X=z×standard deviation+meanX = z \times \text{standard deviation} + \text{mean}.
  5. Plug in values: Plug in the values: X=−0.842×10+53X = -0.842 \times 10 + 53.
  6. Calculate X: Calculate the value of X: X=−8.42+53X = -8.42 + 53.
  7. Round to nearest thousandth: X=44.58X = 44.58, but we need to round to the nearest thousandth.
  8. Round to nearest thousandth: X=44.58X = 44.58, but we need to round to the nearest thousandth.Rounded value: X=44.580X = 44.580.

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