Answer to Question #231836 in Statistics and Probability for sally

Question

hi i need help with this question please and thank you.

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. Find the percentage of students with GPA between 2.00 to 3.00, P (2< X < 3)

Answer 1

$\mu=2.8 \\ \sigma= 0.52 \\ P(2<X<3) = P(X<3) -P(X<2) \\ = P(Z< \frac{3-2.8}{0.52}) -P(Z< \frac{2-2.8}{0.52}) \\ = P(Z< 0.384) -P(Z< -1.538)$

Form table of Z Score

$= 0.6495 -0.0620 \\ = 0.5875 \\ = 58.75 \; \%$