Question

Problem 8: 21 22 12 a. Find the zy that corresponds to the shaded area ai = 0.15 under the standard normal curve. [5 points) b. Find the 22 that corresponds to the shaded area 42 = 0.11 under the standard normal curve. (5 points]

Answer 1

a)

(i) We have , $P(Z>z_1)=0.15$

$\Rightarrow 1-P(Z\leq z_1)=0.15$

$\Rightarrow \Phi( z_1)=1-0.15=0.85$...............(I)

From standard normal distribution table , $\Phi(1.04)=0.85$ ............(II)

From (I) and (II) , we get , $z_1=1.04$

(ii) We have ,

$\Rightarrow P(Z\leq z_2)=0.11$

$\Rightarrow \Phi( z_1)=0.11$

$\Rightarrow 1-\Phi(- z_1)=0.11$

$\Rightarrow \Phi(- z_1)=1-0.11=0.89$...............(I)

From standard normal distribution table , $\Phi(1.23)=0.89$ ............(II)

From (I) and (II) , we get , $z_2=-1.23$

7)

a) We have ,

$P(Z<-1.8)=\Phi(-1.8)=1-\Phi(1.8)=1-0.9641=0.0359$ ; From standard normal distribution table

b) We have ,

$P(-1.1<Z<0.5)=P(Z<0.5)-P(Z<-1.1)$

$=\Phi(0.5)-\Phi(-1.1)=\Phi(0.5)-[1-\Phi(1.1)]$

$=0.6915-1+0.8643=0.5558$ ; From standard normal distribution table