Question

Number of students, mean and standard deviation of std X students of three different schools are as follows -

Govt Boys High School: N = 60, Mean = 38, SD = 5.2

Govt Girls High School: N = 50, Mean = 42, SD = 4.8

Govt Coeducation High School: N = 80, Mean = 46, SD = 6.1

I. Find how many students of Govt Boys High School are above the mean of Govt Girls High School

II. Find how many students of Govt Boys High School are above the mean of Govt Coeducation High School.

III. Find how many students of Govt Girls High School are above the mean of Govt Coeducation High School

IV. Find how many students of Govt Coeducation High School are below the mean of Govt Boys High School 

Answer 1

I.

$z=\frac{\mu_2-\mu_1}{\sigma_1}=\frac{42-38}{5.2}=0.77$

$P(z>0.77)=1-0.7794=0.2206$

number of students of Govt Boys High School are above the mean of Govt Girls High School:

$N_1\cdot P(z>0.77)=60\cdot0.2206=13$

II.

$z=\frac{\mu_2-\mu_1}{\sigma_1}=\frac{46-38}{5.2}=1.54$

$P(z>1.54)=1-0.9382=0.0618$

number of students of Govt Boys High School are above the mean of Govt Coeducation High School:

$N_1\cdot P(z>1.54)=60\cdot 0.0618=4$

III.

$z=\frac{\mu_2-\mu_1}{\sigma_1}=\frac{46-42}{4.8}=0.83$

$P(z>0.83)=1-0.7967=0.2033$

number of students of Govt Girls High School are above the mean of Govt Coeducation High School:

$N_1\cdot P(z>0.83)=50\cdot 0.2033=10$

IV.

$z=\frac{\mu_2-\mu_1}{\sigma_1}=\frac{38-46}{6.1}=-1.31$

$P(z<-1.31)=0.0951$

number of students of Govt Coeducation High School are below the mean of Govt Boys High School:

$N_1\cdot P(z<-1.31)=80\cdot 0.0951=8$