Question

Find each of the following percentile points and draw the appropriate normal

curve. Complete your procedures.

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

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

3. The results of the entrance examination for freshmen are normally distributed

with 𝑥 = 85 and 𝑠 = 12.5. What is the percentile rank of a score of 92?

Answer 1

1.

z-score is 2.33 for 99 percentile

2.

z-score = 1.65

3.

Since $\mu=85$ and $\sigma =12.5$ we have:

$P (X>92) = P(X-\mu>92-85) = P(\dfrac{X-\mu}{\sigma}>\dfrac{92-85}{12.5})$

Since $\dfrac{X-\mu}{\sigma}$ and $\dfrac{92-85}{12.5}$ = 0.56 we have:

P(X > 92) = P(Z > 0.56)

Use the standard normal table to conclude that

P(Z > 0.56) = 0.2877