, which is the IQ score separating the bottom 10% from the top 90%.

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Let y corresponding iq. y is normally distributed, E(y)=100, σ(y) = 15. p10 is the 10th percentile, the value that left 10% of the population below, or P(y<p10) = 0.1 From the normal distribution table, P(Z<z)=0.9 when z=1.282, then P(Z>-z) = 0.1 p10 = E(y) - 1.282 σ(y) = 80.77

hence the iq =80.77

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