Question

The scores of a reference population on the Wechsler Intelligence Scale for Children (WISC) are normally distributed with mean = 100 and standard deviation = 15.

What score would represent the 25th percentile?

Answer 1

Supposing X is the variable we call "score" and K the score you want to find. Then the problem is find K that satisfies,
\[P(X\leq K)=0.25\ \ \text{with}\ \ N(100,15)\]
Now you should standarize the variables,
\[P\left(Z\leq \frac{K-100}{15}\right)=0.25\]The last step is using the normal distribution table, where you will se that,
\[\frac{K-100}{15}=-0.68\]From this point you can find K.