Tail probability of a normal variable by symmetry from a shaded central area, and its standard deviation
Tail probability of a normal variable by symmetry from a shaded central area, and its standard deviation
7 marks
The random variable \(X\) is normally distributed with mean \(140\). In the diagram below, the shaded region between \(131\) and \(140\) represents \(36\%\) of the distribution.
- Find \(\mathrm{P}(X<131)\).[2]
- Find the standard deviation of \(X\).[5]
Solution:
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Answer:(a) \(0.14\) (b) \(\sigma=8.33\)
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