Giventhat,μ=48,σ=5,n=100,then,i)P(43<x<53)=P(543−48<Z<553−48)=P(−1<Z<1)=2P(0<Z<1)=2(0.3413)=0.6826∴number of students=0.6826×100=68.26≈69ii)P(x>40)=P(Z>540−48)=P(Z>−1.6)=0.5+P(0<Z<1.6)=0.5+0.4452=0.9452∴number of students=0.9452×100=94.52≈95iii)P(x>50)=P(Z>550−48)=P(Z>0.4)=0.5−P(0<Z<0.4)=0.5−0.1554=0.3446∴number of students=0.3446×100=34.46≈35
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