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Normal distribution: Area above or below a point

AP.STATS: VAR‑2 (EU), VAR‑2.B (LO), VAR‑2.B.3 (EK) CCSS.Math: HSS.ID.A.4
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A set of magical wand prices are normally distributed with a mean of 50 dollars and a standard deviation of 4 dollars. A blackthorn wand has a price of 45, point, 20 dollars.
What proportion of wand prices are lower than the price of the blackthorn wand?
You may round your answer to four decimal places.
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text