Answer to Question #173724 in Statistics and Probability for Rustom

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