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Complete the statement. Round your answer to the nearest thousandth.\newlineIn a population that is normally distributed with mean 4343 and standard deviation 55, the bottom 80%80\% 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 4343 and standard deviation 55, the bottom 80%80\% of the values are those less than ___.
  1. Find z-score for 8080%: We need to find the z-score that corresponds to the bottom 80%80\% of a normal distribution.
  2. Use z-table to find z-score: Using a z-table, we find that the z-score for 80%80\% is approximately 0.840.84.
  3. Calculate XX using z-score formula: Now we use the z-score formula: z=X−meanstandard deviationz = \frac{X - \text{mean}}{\text{standard deviation}}. We rearrange it to solve for XX: X=z×standard deviation+meanX = z \times \text{standard deviation} + \text{mean}.
  4. Plug in values and solve: Plug in the values: X=0.84×5+43X = 0.84 \times 5 + 43.
  5. Calculate final value: Calculate the value: X=4.2+43X = 4.2 + 43.
  6. Round to nearest thousandth: X=47.2X = 47.2.
  7. Round to nearest thousandth: X=47.2X = 47.2.Round the answer to the nearest thousandth: The value is 47.20047.200.

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