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%
