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Complete the statement. Round your answer to the nearest thousandth.\newlineIn a population that is normally distributed with mean 7272 and standard deviation 88, the bottom 10%10\% 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 7272 and standard deviation 88, the bottom 10%10\% of the values are those less than ___.
  1. Find z-score for bottom 10%10\%: We need to find the z-score that corresponds to the bottom 10%10\% of a normal distribution.
  2. Use z-table to find −1.28-1.28: Using a z-table, we find that the z-score for the bottom 10%10\% is approximately −1.28-1.28.
  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. Solve for X: Rearrange the formula to solve for X: X=z×standard deviation+meanX = z \times \text{standard deviation} + \text{mean}.
  5. Substitute values in formula: Plug in the values: X=−1.28×8+72X = -1.28 \times 8 + 72.
  6. Calculate X: Calculate the value of X: X=−10.24+72X = -10.24 + 72.
  7. Round to nearest thousandth: X=61.76X = 61.76, but we need to round to the nearest thousandth.
  8. Final answer: The final answer, rounded to the nearest thousandth, is 61.76061.760.

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