Answer to Question #213793 in Statistics and Probability for Violet

Question

Find each of the following percentile points under the normal curve.

1.P98

2.P80

3.P64

4.P42

5.P30

Answer 1

$P_{98}$ is a such x, that $P(X\leq x)=0.98$, where X is a standard normal random variable.

By using the tables of quantiles of standard normal distribution we find that $P_{98}=2.054$

Similarly, $P_{80}=0.842$ and $P_{64}=0.358$.

But the values $P_{42}$ and $P_{30}$ one can not get from the tables directly, since these values are negative.

In these cases one should use the formula $P_k=-P_{100-k}$.

Hence $P_{42}=-P_{58}=-0.202$ and $P_{30}=-P_{70}=-0.524$.