Question

In a college, the results of a ministry exam were distributed normally with an average of 70 and a variance of 100. Four students meet after receiving their grades and discuss the exam.
a) What is the expected value and its Standard deviation of the mean of these four students? Give the best possible value with the information you have been given.
b) What is the probability that the mean of these four students is between 60 and 80?
c) What proportion of college students failed?(below 60)
d) What is the expected value and its Standard deviation of the proportion of those who failed(below 60) among these four students?

Answer 1

let Score is X so

E(X)=70 Var(X)=100 this gives SD(X) =square root of Var(X) =10

sample size =n=4

let Sample mean is M

a)

E(M)=E(X)=70

b)

we have to find P(60<M<80)

now

c)

we have to find P(X<60)

now

d)

Here n=4

probability of fail=p=0.159

Expected value=n*p=4*0.159=0.636~1