Standard normal probability above a negative value and an upper bound from a given central probability

Standard normal probability above a negative value and an upper bound from a given central probability

4 marks

The random variable \(Z\) follows the standard normal distribution, \(Z\sim\mathrm{N}(0,1)\).

  1. Find \(\mathrm{P}(Z>-0.8)\).[1]

The constant \(b\) is such that \(\mathrm{P}(-0.8<Z<b)=0.6\).

  1. On the axes below, shade the region whose area represents \(\mathrm{P}(-0.8<Z<b)\), marking \(b\) on the \(z\)-axis.[1]
  2. Hence, or otherwise, find \(b\).[2]

Solution:

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Answer:(a) \(0.788\) (b) region under the curve between \(z=-0.8\) and \(z=b\) (with \(b>0\)) shaded (c) \(b=0.885\)

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