Inequalities invovling Normal Distribution I

Inequalities invovling Normal Distribution I

Given that \(X\sim N\left( -3,8 \right)\). Find the range of \(k\) for

  1. \(\mathrm{P}\left( X>k \right)<0.4\)
  2. \(\mathrm{P}\left( X>k \right)>0.65\)
  3. \(\mathrm{P}\left( X < k \right)<0.8\)
  4. \(\mathrm{P}\left( X<k \right)>0.57\)

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Answer:(a) k > -2.28 (b) k < -4.09 (c) k < -0.620 (d) k > -2.50

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