6.14.2005

Q&A: What's the cutoff for the bottom 10% of an exam...

...with scores normally distributed with m = 80 and s = 5?

A: P(X<73.6) = 10%

  • In Excel: z = NORMSINV(10%) = -1.28.
    • A z-score of -1.28 means that the original score/observation is 1.28 standard deviations below, not above, the mean.
  • Since z = (X - m)/s, X = z*s + m = -1.28*5 + 80 = 73.6.

Category: Quantitative Analysis > Probability

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