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Complete the statement. Round your answer to the nearest thousandth.\newlineIn a population that is normally distributed with mean 6363 and standard deviation 77, the bottom 30%30\% 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 6363 and standard deviation 77, the bottom 30%30\% of the values are those less than ___.
  1. Calculate z-score for 3030th percentile: To find the value that separates the bottom 30%30\% from the rest, we need to use the z-score formula for the 3030th percentile.
  2. Find z-score using formula: The z-score for the 30th30^{\text{th}} percentile can be found using a z-table or a calculator with inverse normal function. Let's assume the z-score for the 30th30^{\text{th}} percentile is approximately −0.52-0.52.
  3. Use z-score formula: Now we use the z-score formula: X=μ+zσX = \mu + z\sigma, where XX is the value we're looking for, μ\mu is the mean, zz is the z-score, and σ\sigma is the standard deviation.
  4. Plug in values: Plug in the values: X=63+(−0.52)(7)X = 63 + (-0.52)(7).
  5. Calculate result: Calculate the value: X=63−3.64X = 63 - 3.64.
  6. Round to nearest thousandth: X=59.36X = 59.36, but we need to round to the nearest thousandth.
  7. Final answer: The final answer, rounded to the nearest thousandth, is 59.36059.360.

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