Question

i need help with this second question two, theyre similar.

X represents the Grade Point Average (GPA) of students at a private college which follows normal distribution with mean of 2.8 and standard deviation of 0.52. If top 5% of the students will receive special awards, what is the minimum GPA required to qualify for the award?

Answer 1

$\mu=2.8 \\ \sigma=0.52 \\ P(X<x) = 1-0.05 = 0.95 \\ P(Z< \frac{x -2.8}{0.52}) = 0.95$

From table of Z Score

$\frac{x -2.8}{0.52} = 1.65 \\ x -2.8 = 0.52 \times 1.65 \\ x = 2.8 + 0.858 \\ x = 3.658$

Answer: The minimum GPA required to qualify for the award is 3.66.