1. ## Normal probability calculations

Let X~N(0,1) . Compute each in terms of function ϕ. (0 being mu and 1 being delta^2)
And evaluate it numerically.

1. P(X<=-5)
2. P(-2<=X<=7)
3. P(X>=3)

for the first one i get
ϕ(-5)

But how do i evaluate it?

this is a wiki page on it
Normal distribution - Wikipedia, the free encyclopedia

2. #1 is correct.

#2 $\displaystyle \phi (7) - \phi ( - 2)$

#3 Is for you to do.

3. but dont i need to get numerical values, since the question says "And evaluate it numerically"...?

and for c would it be

ϕ(inf)-ϕ(3)
or just
1-ϕ(3)

4. Originally Posted by Sneaky
but dont i need to get numerical values, since the question says "And evaluate it numerically"...?
Sorry, I don't do numbers.

5. ok, is c
ϕ(inf)-ϕ(3) ?
i dont understand what ϕ(inf) means?

6. For the second:
2. P(-2<=X<=7)=P(-2<=Z<=7)=P(Z<=7)-P(Z<=-2)=P(Z<=7)-P(Z>2)=P(Z<=7)-(1-P(Z<=2))

7. Originally Posted by Sneaky
ok, is c
ϕ(inf)-ϕ(3) ?
i dont understand what ϕ(inf) means?
$\displaystyle \displaystyle\lim _{x \to \infty } \phi (x) = 1$.