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Complete the statement. Round your answer to the nearest thousandth.\newlineIn a population that is normally distributed with mean 8787 and standard deviation 1111, the bottom 70%70\% 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 8787 and standard deviation 1111, the bottom 70%70\% of the values are those less than ___.
  1. Find Z-score for 7070%: To find the value that separates the bottom 70%70\% from the rest, we need to use the z-score table to find the z-score that corresponds to a cumulative probability of 0.700.70.
  2. Lookup Z-score in table: Looking up 0.700.70 in the z-score table, we find that the closest z-score is approximately 0.520.52.
  3. Calculate X using formula: Now, we use the z-score formula to find the value XX: Z=X−meanstandard deviationZ = \frac{X - \text{mean}}{\text{standard deviation}}. Rearranging the formula to solve for XX gives us X=Z×standard deviation+meanX = Z \times \text{standard deviation} + \text{mean}.
  4. Plug in values for X: Plugging in the values, we get X=0.52×11+87X = 0.52 \times 11 + 87.
  5. Round to nearest thousandth: Calculating this, X=5.72+87X = 5.72 + 87.
  6. Round to nearest thousandth: Calculating this, X=5.72+87X = 5.72 + 87.So, X=92.72X = 92.72. But we need to round to the nearest thousandth, which doesn't change the value in this case since it's already at the thousandth place.

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