Question

Human iq scores are approximately normally distributed with mean 100 and standard deviation 15. determine the minimum iq scores for the top 5% of the population.

Answer 1

To solve this problem, we make use of the z statistic. A population of 5% means that we are looking for the population at >95%, P = 0.95. Using the standard distribution tables for z, a value of P = 0.95 indicates a value of z of z = 1.645

Now given the z and standard deviation s and the mean u, we can calculate for the value of IQ of the top 5% (x):

x = z s + u

x = 1.645 (15) + 100

x = 24.675 + 100

x = 124.675

Therefore the minimum iq score for the top 5% of the population is around 124.675