Answer to Question #345787 in Statistics and Probability for wew

Question

A division wide aptitude test in mathematics was conducted to 1000 pupils. The mean of the test is 58 and the standard deviation is 12. The scores also approximate the normal distribution. What is the minimum score to belong the upper 20% of the group?

Answer 1

Let the minimum score required to be in the upper 20% of the group be c. Then

$P(X \ge c)=0.20$

$P(X<c)=1-0.2=0.80$

$P(Z<\frac{c-58}{12})=0.8$

Then we found z-value from p from z-table:

So,

$\frac{c-58}{12}=0.84$

c-58=10.08

c=68.08