Probability below a value for a normally distributed waiting time and the value exceeded with a given probability

Probability below a value for a normally distributed waiting time and the value exceeded with a given probability

6 marks

At a clinic, the waiting time, \(T\) minutes, of a patient is normally distributed with mean \(42\) minutes and standard deviation \(6\) minutes.

  1. One patient is chosen at random. Find the probability that this patient waits less than \(50\) minutes.[3]
  2. It is given that \(\mathrm{P}(T>k)=0.7257\). Find the value of \(k\).[3]

Solution:

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Answer:(a) \(0.909\) (b) \(k=38.4\)

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