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Complete the statement. Round your answer to the nearest thousandth.\newlineIn a population that is normally distributed with mean 6464 and standard deviation 1313, the bottom 40%40\% 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 6464 and standard deviation 1313, the bottom 40%40\% of the values are those less than ___.
  1. Find Z-Score: We need to find the z-score that corresponds to the bottom 40%40\% of a normal distribution.
  2. Use Z-Table: Using a z-table, we find that the z-score for the bottom 40%40\% is approximately −0.25-0.25.
  3. Z-Score Formula: Now we use the z-score formula: z=X−meanstandard deviationz = \frac{X - \text{mean}}{\text{standard deviation}}. We need to solve for XX, which represents the value we're looking for.
  4. Plug in Values: Plugging in the values we get: −0.25=(X−64)13-0.25 = \frac{(X - 64)}{13}.
  5. Isolate X: Multiplying both sides by 1313 to isolate XX, we get: −0.25×13=X−64-0.25 \times 13 = X - 64.
  6. Calculate Left Side: Calculating the left side: −0.25×13=−3.25-0.25 \times 13 = -3.25.
  7. Solve for X: Adding 6464 to both sides to solve for XX, we get: X=64−3.25X = 64 - 3.25.
  8. Calculate Final Value: Calculating the final value: X=60.75X = 60.75.

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