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Complete the statement. Round your answer to the nearest thousandth.\newlineIn a population that is normally distributed with mean 5050 and standard deviation 2020, the bottom 20%20\% 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 5050 and standard deviation 2020, the bottom 20%20\% of the values are those less than ___.
  1. Find z-score for 2020%: We need to find the z-score that corresponds to the bottom 20%20\% of a normal distribution.
  2. Use z-table: Using a z-table, we find that the z-score for the bottom 20%20\% is approximately −0.842-0.842.
  3. Apply 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: −0.842=X−5020-0.842 = \frac{X - 50}{20}.
  5. Isolate X: Multiplying both sides by 2020 to isolate XX, we get: −0.842×20=X−50-0.842 \times 20 = X - 50.
  6. Do multiplication: Now we do the multiplication: −16.84=X−50-16.84 = X - 50.
  7. Solve for X: Adding 5050 to both sides to solve for XX, we get: X=50−16.84X = 50 - 16.84.
  8. Calculate final value: Finally, we calculate XX: X=33.16X = 33.16.

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