Question

14. Consider the intelligence quotient (1.Q.). It is known that IQ's N100,256). If a person were selected a random, (a) What is the probability that his or her I would be below 1207 P[x < 120] =PCK <120, MJ = P[Z<!2010 {P[221.25) be above 120? [PE74420718.89 PL x 120 = 1-PLX212 1-0.89 = | x Spo). Q.1 | (c) What is the probability that his or her IQ would be between 90 and 1057 2 -X- 4 90-100_ 1 (2="0.625 x =105=2=8-4=los-100 (d) What is the probability that his or her I would be below 90? 16 X-ULOV Th=(2=0.3125 d be below 90? 16 12 70-100 - 240.625 P[-0.628240,3125 (e) What is the 95th percentile2 = 0.266 P (-0625<2<d+ ROCZE 0.367 +6,311 0,67. (f) What is the 3rd quartile? moon of 6.3 and a standard deviatior

Answer 1

solution Here mean(M)=100, S.D(~) = 8256 = 16 we know that z= x-4 a) for x=120, 2= 120 - 100 = 1.25 P (below 120)=P(x2 120 =P/221.25 = 10.8944 | b) p (above 120)=P(&>120)=P(2>1.25) =1-P122 1-25) = 1-0.89uu = 0.1054 o for x=90, 2= 90-100 = -0.625 687 2 = 105, Z = 105-100 – 0-3125 P(Between 90 & 105)=P(90<x< 105 =P(-0.625€ 2 € 0.3125 =P(240-3125)-Plze-0.625)=0-6227-'0-266 = 8.36170-3567 d) P/ below 90)=P(2440)=P/22 -0.625) = (0.266] e the z- value at 95th porcentile is 1.6us then 95th percentile = "+16 uso 16 = 100 +1.6us (16) = 127-32 f) . The Qz = ut 0.67us = 100+ 0.6745 (16) = 110.7927