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H2 Maths Notes
H2 Maths 6.3 - Normal Distribution: Finding Unknown Parameters
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Given P(X < 40) = 0.1587 and P(X > 60) = 0.0668, find mu and sigma for X ~ N(mu, sigma^2).
First condition: P(Z < z) = 0.1587 gives z = -1, so (40 - mu) / sigma = -1, that is mu - sigma = 40.
Second condition: P(Z < z) = 0.9332 gives z = 1.5, so (60 - mu) / sigma = 1.5, that is mu + 1.5 sigma = 60.
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