Answer to Question #189838 in Statistics and Probability for LE10

Question

What is the equivalent of P (6 ≤ X ≤ 8)?

A) P(X ≤ 8) - P(X ≤ 6)

B) P(X ≤ 8) - P(X ≤ 5)

C) 1- [P(X ≤ 8) + P(X ≤ 6)]

D) P(X ≤ 8) + P(X ≤ 6)

Choose The Right answer

Answer 1

$P(6\leq X\leq8)=P(\dfrac{6-8}{2}\leq Z<\dfrac{8-8}{2})=P(-1\leq Z<0)=0.5-0.1587=0.3423$

$P(X\leq 8)=P(Z<\dfrac{8-8}{2})=P(Z<0)=0.5\\P(X\leq 6)=P(Z<\dfrac{6-8}{2})=P(Z<-1)=0.1587$

So, $P(6\leq X\leq 8)=P(X\leq 8)-P(X\leq 6)$

Answer: Option A is correct