Question

Critical reading SAT scores are distributed as N(480, 99). Find:

a) Find the SAT score at the 75th percentile

b) Find the SAT score at the 25" percentile

Answer 1

Solution:

Given information:
μ = 480, σ = 99

(a) Here we need z-score has 0.75 area to its left. From z-table 0.67 has approximately 0.75 area to its left.
Let X is a random variable shows the distribution of SAT score. So required score is
z = X - μ/σ
0.67 = X - 480/99
X = 0.67*99+ 480
= 546.33
Hence, required SAT score at 75th percentile is 546.33.
-------------------------------------------
(b) Here we need z-score has 0.25 area to its left. From z-table -0.67 has approximately 0.25 area to its left.
Let X is a random variable shows the distribution of SAT score. So required score is
z = X - μ/σ
-0.67 = X - 480/99
X = -0.67*99+ 480
= 413.67
Hence, required SAT score at 25th percentile is 413.67.