Question

1.   The height of grade 1 pupils is approximately normally distributed with µ = 45 inches and s = 2.

1.   If an individual pupil is selected at random, what is the probability that he or she has a height of 42 and 47?

Answer 1

X ~ $N(45, 2^2)$

$P(42<X<47)=P(42<N(45,2^2)<47)=P(42<45+2N(0,1)<47)=\\=P(-1.5<N(0,1)<1)=P(N(0,1),1)<1)-P(N(0,1)<-1.5)=\\=0.84134-0.06681=0.77453$