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# Normal Distribution watch

1. Bah... I left my textbook at college and have no notes on this.

The percentage, X%, of a certain metal in an alloy can be modelled as having a normal distribution with mean 70 and standard deviation σ. It is given that P(X>77) = 0.0808. Find the value of σ.

Cheers. (Almost worthless rep available.)
2. The percentage, X%, of a certain metal in an alloy can be modelled as having a normal distribution with mean 70 and standard deviation σ. It is given that P(X>77) = 0.0808. Find the value of σ.
X ~ N(70, σ²)

P(X > 77) = 1 - Φ((77-70)/σ ) = 0.0808
............. = 1 - 0.0808 = Φ((77-70)/σ )
............. = 0.9192 = Φ(7/σ )
............. = Φ-1(0.9192) = 7/σ
............. = 1.398 = 7/σ (from tables)
............. = σ = 7/1.398 ≈ 5.007

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Updated: January 27, 2006
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