Answer to Question #332554 in Statistics and Probability for Nyx

Question

Apply the Normal Curve concepts to solve each of the following. Show your complete solution

and illustration.

2. Most graduate schools of business require applicants for admission to take the Graduate

Management Admission Council’s GMAT examination. Scores on the GMAT are roughly

normally distributed with a mean of 506 and a standard deviation of 96.

a. What is the probability of an individual scoring above 520? (with illustration)

b. What is the probability of an individual scoring below 506? (with illustration)

c. What is the probability of an individual scoring from 387 to 712? (with illustration)

3. Given 𝜇=45, and 𝜎=5.5.

a. What is the raw score when 𝑧=−1.57?

b. What is the raw score when 𝑧=2.09?

c. What is the raw score when −0.48<𝑧 <1.4?

d. What is the raw score when −2.17<𝑧 <1.79?

e. What is the raw score when 𝑧=0.09?

Answer 1

2. $P(X>520)=1-P(X<520)=1-P(Z<\frac{520-506}{96})=1-P(Z<0.15)=1-0.5596=0.4404$

$P(X<506)=P(Z<\frac{506-506}{96})=P(Z<0)=0.5$

$P(387<X<712)=P(\frac{387-506}{96}<Z<\frac{712-506}{96})=P(-1.24<Z<2.15)=0.9842-0.1075=0.8767$

3.$Z=\frac{x-\mu}{\sigma}$

$x=Z\sigma+\mu$

a.x=-1.57x5.5+45=36.37

b. x=2.09x5 .5+45=56.50

c.x₁=-0.48x5.5+45=42.36

x₂=1.4x5.5+45=52.7

d.x₁=-2.17x5.5+45=33.07

x₂=1.79x5.5+45=54.85

e. x=0.09x5.5+45=45.50