Probability above a value for a normal variable and the value exceeded with a given probability, shown on a sketch
Probability above a value for a normal variable and the value exceeded with a given probability, shown on a sketch
8 marks
The random variable \(X\) is normally distributed with mean \(64\) and variance \(25\).
- Find \(\mathrm{P}(X>58)\).[3]
- It is given that \(\mathrm{P}(X>k)=0.2\).
- On the diagram below, mark \(k\) and shade the region whose area is \(0.2\).
- Find the value of \(k\).[5]
Solution:
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Answer:(a) \(0.885\) (b)(i) \(k\) to the right of \(64\), upper tail shaded (b)(ii) \(k=68.2\)
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