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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 77, the bottom 90%90\% 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 6464 and standard deviation 77, the bottom 90%90\% of the values are those less than ___.
  1. Find Z-Score for 9090%: To find the value that separates the bottom 90%90\% from the top 10%10\%, we need to use the z-score table to find the z-score that corresponds to a cumulative probability of 0.900.90.
  2. Lookup Z-Score: Looking up the z-score for a cumulative probability of 0.900.90 in the z-score table, we find that the z-score is approximately 1.281.28.
  3. Use Z-Score Formula: Now we use the z-score formula to find the value: 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=64+(1.28)(7)X = 64 + (1.28)(7).
  5. Calculate Value: Calculate the value: X=64+8.96X = 64 + 8.96.
  6. Round to Nearest Thousandth: X=72.96X = 72.96, but we need to round to the nearest thousandth.
  7. Final Answer: The final answer, rounded to the nearest thousandth, is 72.96072.960.

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