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Complete the statement. Round your answer to the nearest thousandth.\newlineIn a population that is normally distributed with mean 6666 and standard deviation 2020, the bottom 40%40\% 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 6666 and standard deviation 2020, the bottom 40%40\% of the values are those less than ___.
  1. Find z-score for 4040\%: First, we need to find the z-score that corresponds to the bottom 40%40\% of a normal distribution.
  2. Calculate z-score: Using a z-table, we find that the z-score for the bottom 40%40\% is approximately −0.25-0.25.
  3. Use z-score formula: Now, we use the z-score formula: z=X−μσz = \frac{X - \mu}{\sigma}, where XX is the value we're looking for, μ\mu is the mean, and σ\sigma is the standard deviation.
  4. Solve for X: We rearrange the formula to solve for X: X=z⋅σ+μX = z \cdot \sigma + \mu.
  5. Plug in values: Plug in the values: X=−0.25×20+66X = -0.25 \times 20 + 66.
  6. Calculate X: Calculate the value: X=−5+66X = -5 + 66.
  7. Final result: X=61X = 61.

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