Answer to Question #317169 in Statistics and Probability for Xhely

Question

1. Find the 99th percintile of the normal curve.

2. Find the upper 5% of the normal curve.

3.Find the 92nd percintile rank of the normal curve.

Answer 1

From z-table:

1. 99^th percentile $\approx$ 2.33 ($P(Z\leq2.33)=0.99010$).

2. The upper 5% of the normal curve:

$P(Z\leq1.645)\approx0.95, \\P(Z\geq1.645)\approx1-0.95=0.05.$

We look for 0.9500 inside the z-table.

Although 0.9500 does not appear, both 0.9495 and 0.9505 do, corresponding to z = 1.64 and 1.65, respectively.

Since 0.9500 is halfway between the two probabilities that do appear, we will use 1.645 as the 95th percentile.

3. 92^th percentile $\approx$ 1.405

We look for 0.9200 inside the z-table.

Although 0.9200 does not appear, both 0.9192 and 0.9207 do, corresponding to z = 1.40 and 1.41, respectively.

Since 0.9200 is approximately halfway between the two probabilities that do appear, we will use 1.405 as the 92th percentile.