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Complete the statement. Round your answer to the nearest thousandth.\newlineIn a population that is normally distributed with mean 55 and standard deviation 1414, 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 55 and standard deviation 1414, the bottom 90%90\% of the values are those less than ___.
  1. Find z-score for 9090%: Find the z-score for 9090\%. Using a z-table or calculator, the z-score for 9090\% is approximately 1.2821.282.
  2. Use z-score formula: Use the z-score formula to solve for XX.
    mean (μ\mu): 55
    standard deviation (σ\sigma): 1414
    z-score (ZZ): 1.2821.282
    Z=X−μσZ = \frac{X - \mu}{\sigma}
    1.282=X−5141.282 = \frac{X - 5}{14}
  3. Multiply by standard deviation: Multiply both sides by the standard deviation.\newline14×1.282=X−514 \times 1.282 = X - 5\newline17.948=X−517.948 = X - 5
  4. Add mean to solve for X: Add the mean to both sides to solve for XX.X=17.948+5X = 17.948 + 5X=22.948X = 22.948

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