Question

Intelligence scores are distributed approximately normally with μ = 100 and σ = 15. In each
part of this question, use two places after the decimal point for z scores and four places after the decimal point
for proportions. For each part (except part e), include an appropriate sketch

f) How low must an intelligence score be to be in the lowest 15%?

g) How low must the mean of a random sample of 9 intelligence scores
be to be in the lowest 15%?

h) How low must the mean of a random sample of 25 intelligence
scores be to be in the lowest 15%?

i) How low must the mean of a random sample of 100 intelligence
scores be to be in the lowest 15%?

Answer 1

- Normal (4=100, 6= 15) 0.15 F ie P(x&c) = 0.15 e-scare for 0.15 =-1.03643 TIIN P(x-M LC-100) = 0.15 IS 15 ol pe X-100 = 260.15) x= 100+ 15210.15) x= 100+15+(-1.03643) x=84.45 # 84.45 score in lowust 15t. Till g n=9 x-(1,02) InN (MAG) 100 tis x Z10.15) F= 100+ 15 x 210.15) *= loot Is x² X = 94.824 h n=25 x=loot 15 XZ 10.15) Ty=96.89 niloo X=100+ 15 x2(0.15) 25 loo =98.457