Answer to Question #202859 in Statistics and Probability for Billy

Question

A division-wide aptitude test in Mathematics was conducted to 1000 pupils. The mean of the rest is 58 and the standard deviation is 12. The scores also approximate the normal distribution. What is the minimum scores to belong to the upper 10% is the group?

Answer 1

$\mu=58 \\ \sigma=12$

Let the minimum score required to be in the upper 10% of the group be c. Then,

$P(X≥c)=0.10 \\ P(X<c) = 1 -0.10 = 0.90 \\ P(Z< \frac{c-58}{12})=0.90 \\ \frac{c-58}{12} = 1.281 \\ c-58=15.372 \\ c = 73.372$

Therefore, the minimum score required to belong to the upper 10 % of the group is 73.372.