Question

In "Testing the Science of Intelligence" Newsweek (October 24, 1994), Geofrey Cowley reported that "IQ's for a whole population can be arrayed on a single graph. Roughly two-thirds of all Americans fall between 85 and 115, in the fat midsection of the bell-shaped curve, and 95 percent score between 70 and 130."(p. 57) 2. If IQs are distributed normally with a mean of 100 and standard deviation of 15, then: a. what is the lowest IQ of the top 25% of people? Approximately 40% of the population has an IQ less than 100, but greater than what value? b.

Answer 1

(2) From the given informati on, let X be the IQs are distributed normally with mean μ 100, and standard deviation σ 15 (a) P(X > x)-2596-0.25 x-1000.75 PZ100 From, normal area tables the area to the left of Z -0.675 is approximately 0.750 x-100 0.675 x 100+0.675x15 110.125110 The lowest IQ of the top 25% of people is approximately 110 (b) P(x < X < 100)-40%-0.40 x- 100 100-100 0.40 x-100 <Z <0 0.40 P(-z <Z <0) 0.40 P(0 <Z <z) 0.40 by symmetric property →P(-00 < Z <z) = 0.5+0.40 = 0.90 From, normal area tables the area to the left of z-1.28 is approximatley 0.90 Therefore, z - score with lower tail is -1.28 x-100 =-1.28→x= 100-12815)-80.8-80 Therefore, approximately 40% of the population has an IQ les s than 1 00 but greater than 80