Unknown normal mean and standard deviation from a lower-tail probability and a conditional probability
Unknown normal mean and standard deviation from a lower-tail probability and a conditional probability
7 marks
The times taken by members of a puzzle club to solve a particular puzzle are normally distributed with mean \(\mu\) minutes and standard deviation \(\sigma\) minutes.
A member chosen at random has probability \(0.25\) of solving the puzzle in less than \(12\) minutes.
Given that a randomly chosen member takes less than \(12\) minutes, the probability that they take less than \(9\) minutes is \(0.32\).
Find the value of \(\mu\) and the value of \(\sigma\).[7]
Solution:
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Answer:\(\mu=14.8\text{ minutes},\ \sigma=4.11\text{ minutes}\)
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