Answer:

a. 15.866%

b. 2.275%

c. 34.134%

d. 81.860%

Step-by-step explanation:

In this question, we shall be using the formula for z-score a couple of times.

Mathematically;

z-score = (score - mean)/SD

where mean = 547 and SD = 100

A. % of GMAT scores 647 or higher

Mathematically;

z-score = (647-547)/100 = 100/100 = 1

P( z ≥ 1) = 1 - P( z < 1)

= 1 - 0.84134 = 0.15866 which is same as 15.866%

B. % of GMAT scores 747 or higher

z-score = (747-547)/100 = 200/100 = 2

So the probability is P(z ≥ 2) = 1 - P( z <2) = 1- 0.97725 = 0.02275 which is same as 2.275%

C. between 447 and 547

z-score for 447 = (447-547)/100 = -100/100 = -1

For 547 = (547-547)/100 = 0/100 = 0

So the probability is;

P( -1 < z < 0) = P(z < 0) - P(z < -1) = 0.5 - 0.15866 = 0.34134 which is 34.134%

D. between 347 and 647

z-score for 347 = (347-547)/100 = -200/100 = -2

z-score for 647 = (647-547)/100 = 100/100 = 1

So the probability is;

P(-2 < z < 1) = P(z < 1) - P(z < -2) = 0.84134 - 0.02275 = 0.81859 = 81.86%