Question

The results of a nationwide aptitude test in mathematics are normally distributed with the mean=63 and standard deviation=5. What is the probability that students get the score in between 50 to 70?

Answer 1

X ~ $N(63,5^2)$

$P(50<X<70)=P(50<N(63,5^2)<70)=P(50<63+5N(0,1)<70)=P(-2.6<N(0,1)<1.4)=P(N(0,1)<1.4)-P(N(0,1)<-2.6)=0.91924-0.00466=0.91458$