Normal Random Variables

Question

Suppose scores on an IQ test are normally distributed with a mean of 100 and a standard deviation of 10.

a) Find the range of scores for the bottom 20% of students. Be sure to complete all three steps and then indicate which applet you used.

b) Find the range of scores for the middle 70% of students. Be sure to complete all three steps and then indicate which applet you used.

Answer 1

Prob( z < k) = 0.2

k = -0.84 per the table. ( I actually used MS Excel)

(x - mean)/stddev = z

x = z * stddev + mean

= -0.84*10 + 100 = 91.6

Prob(z<k) = 0.85

Prob(z<c) = 0.15

Prob( c < z < k) = Prob(z < k) - Prob(z<C) = 0.85 - 0.15 = 0.70

This happens around C=-1.05 and k=1.05

So the range is -1.05*10+100 , 1.05*10 + 100

89.5, 110.5