The time taken, T seconds, to open a graphics programme on a computer is normally distributed with

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The time taken, T seconds, to open a graphics programme on a computer is normally distributed with mean 20 and standard deviation σ.

Given that P(T > 13 | T ≤ 27) = 0.8, find the value of:

a. σ

b. k for which P(T > k) = 0.75.

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