Question

Given population of 5000 scores with mean=86 and standard devation=10. How many scores are between 76 and 86

Answer 1

X ~ N$(86,10^2)$

$P(76<N(86,10^2)<86)=P(76<86+10N(0,1)<86)=P(-1<N(0,1)<0)=P(N(0,1)<0)-P(N(0,1)<-1)=0.5-0.15866=0.34134$

So, there will be approximately 5000*0.34134=1706.7 $\approx$ 1707 such scores