Answer to Question #161250 in Quantitative Methods for Sunny

Question

Assume that the test scores from a college admissions test are normally distributed, with a

mean of 450 and a standard deviation of 100.

a. What percentage of the people taking the test score between 400 and 500?

b. Suppose someone receives a score of 630. What percentage of the people taking the

test score better? What percentage score worse?

c. If a particular university will not admit anyone scoring below 480, what percentage of

the persons taking the test would be acceptable to the university?

Answer 1

We have:

$\mu=450,\sigma=100$

a.

$z_1=\frac{x_1-\mu}{\sigma}=\frac{400-450}{100}=-0.5$

$z_2=\frac{x_2-\mu}{\sigma}=\frac{500-450}{100}=0.5$

$P(400<x<500)=P(-0.5<z<0.5)=2P(z<-0.5)=2\cdot0.3085=61.70\%$

b.

$z=\frac{x-\mu}{\sigma}=\frac{630-450}{100}=1.8$

$P(x<630)=P(z<1.8)=0.9641=96.41\%$

$P(x>630)=P(z>1.8)=1-P(z<1.8)=1-0.9641=0.0359=3.59\%$

c.

$z=\frac{x-\mu}{\sigma}=\frac{480-450}{100}=0.3$

$P(x>480)=P(z>0.3)=1-P(z<0.3)=1-0.6179=0.3821=38.21\%$