Probability and distribution question

[liamlamont]

What is the reason behind flipping the sign and making it 1-P?

 

[Dr.Peterson]

If A is an event, then P(not A) = 1 - P(A), and P(A) = 1 - P(not A).

That is what they are doing, using the complement of "X > 0", which is "X ≤ 0"; but they are also using the fact that this is a continuous distribution, such that P(X = 0) = 0 so that they can just use "X < 0" as the complement.

Why do they need to do this? Because the Excel function they are going to use gives P(X < x), not P(X > x).

 

[Steven G]

Here is an equivalent way of thinking about it. Either x>0 or x< 0 100% of the time. What other option could x be?

Therefore P(x<0) + P(x< 0) = 1. Then P(x<0) = 1 - P(x< 0)

Now follow Dr Peterson's post.