Question

is a standardized test that students usually take before entering graduate s 5. The GRE chool. According to a document, the scores on the verbal portion of the GRE have mean 150 points and standard deviation 8.75 points. Assu ming that these scores are (approximately) normally distributed. a Obtain and interpret the quartiles. b. Find and interpret the 99h percentile.

Answer 1

Mean=150 and std= 8.75

a)Q1: 0.25 => P(Z<x)= 0.25 => Z= -0.67

$Z= \frac{q_1-\mu }{\sigma }=-0.67$

$\frac{q_1-150 }{8.75 }=-0.67=> q_1= 150-5.8625 =144.1375$

Q3: 0.75 ; => P(Z< x) =0.75 => Z= 0.67

$\frac{q_1-150 }{8.75 }=0.67=> q_1= 150+5.8625 =155.8625$

Inter quartile ranges: Q3-Q1= 155.8625- 144.1375= 11.725

b) 99th percentile:

Z(0.99)= 2.326

$Interval: \mu +Z*\sigma => 150+2.326*8,75= 170.3525$