Given m=70,N=1000 S.D ($\sigma$)=5

z=$\frac{X-m}{\sigma}$

$\frac{X-70}{5}$------(1)

A) Between 60 And 75

when X=60

eqn(1) becomes

$z =\frac{60-70}{5}=-2$

when X=75 in equation (1)

$z = \frac{75-70}{5}$=1

$P(60 \le x \le 75)=P(-2 \le z \le 1)$

=Area between z=-2 and z=1

=Area from (z=0 to z=3)+Area from (z=0 to z=1)

=0.4772+0.3413

$P(60\le x\le 75)$=0.8185

Number of students getting marks between 60 and 75

=$N \times p$

=$1000 \times 0.8185$

=818

2) More than 75

when X=75,from equation (1)

z=$\frac{75-70}{5}=1$

$P(x\ge 75)$=$P(z\ge 1)$

Area to the right of z=1

=0.5 -(area between z=0 and z=1)

=0.5-0.3413 =0.1587

therefore number of students getting more then 75 marks= $N \times p$

=$1000 \times 0.1587$

=159