normal distribution with a mean

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Assume that adults have IQ scores that are normally distributed with a mean of 100 and a standard deviation of 15 (as on the Wechsler test). Find P10

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

Jul 3rd, 2015

Thank you for the opportunity to help you with your question!

  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

Please let me know if you need any clarification. I'm always happy to answer your questions.
Jul 3rd, 2015

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Jul 3rd, 2015
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