Given that μ = 100 and σ = 15, what is the IQ that separates the bottom 10% from the other 90% of adults?

• Identify μ, σ and the probability value
• μ = 100, σ = 15
• 10% of adult IQs are less than some x and 90% of adult IQs are more than x
• Lookup the z associated with the probability value.
• P(z < z₁) = 10% = 0.1000 (Remember to look in the body of Table A-2 for the probability value closest to 0.1000, then look to the left column and top row to find the z associated that value.
• 0.1003 is the closest value to 0.10000 in the table. P(z < -1.28) = 0.1003 = 10.03%
• Compute x
• x = 100 - 1.28(15) = 80.8
• Use x to answer the original question
• 10% of adults have an IQ of 80 or less.