Question

The minimum UGPA that would still place a student in the top 10% of UGPAs is

Answer 1

µ = 3.36

sd = 0.18

a) $P(X>x)=0.1$

$or,P(\frac{X-\mu}{\sigma}>\frac{x-\mu}{\sigma})=0.1$

$or,P(Z>\frac{x-3.36}{0.18})=0.1$

$or,1-P(Z<\frac{x-3.36}{0.18})=0.1$

$or,P(Z<\frac{x-3.36}{0.18})=0.9$

$or,\frac{x-3.36}{0.18}=1.28$

or, x = 3.36 + 1.28 * 0.18

or, x = 3.5904

or, x = 3.59

b) Z score for middle 50% = + Z_0.25 = -0.67, 0.67

Z = (X - µ) / sd

lower score = 3.36 - 0.67 * 0.18 = 3.24

upper score = 3.36 + 0.67 * 0.18 = 3.48