answer for Q.1 = 0.0475
answer for Q.2 = 0.1587
1) $n = 10^4$
$p=\frac{1}{10}=0.1$ so, $q = 1-0.1 = 0.9$
mean = $\mu = np = 10^4 \times 0.1 = 10^3$
the standard deviation = $\sigma = \sqrt{npq} = \sqrt{10^4 \times 0.1 \times 0.9} = 30$
on converting it to standard normal distribution, we get : $$z = \frac{ X - \mu }{ \sigma } = \frac{950-1000}{30} = -\frac{5}{3} = -1.67$$
we are given area between $z=0$ and $z=1.67$
this area equals in value with the area between -1.67 and 0
+ the area outside -1.67 and +1.67, both separated areas shown below are EQUAL, due to symmetry in bell curve.
all together makes up 1
therefore, the required area which is, the area below $-1.67$
is given as $=\frac{1-2\times 0.4525}{2}=0.0475$
using the similar technique, for Q.2 we get:
the required area is :
