When you look up the probability in a z-table is that the value less than or less than or equal? For example is it p(z<2.35)=.0094 or is it p(z<=2.35)=.0094? And if they aren't equal then how would you calculate the other one? I would think given any single point has 0 width that it shouldn't matter, but I am not sure.

Nash Frank

Nash Frank

Answered question

2022-07-20

When you look up the probability in a z-table is that the value less than or less than or equal?
For example is it p ( z < 2.35 ) = .0094 or is it p ( z 2.35 ) = .0094?
And if they aren't equal then how would you calculate the other one?
I would think given any single point has 0 width that it shouldn't matter, but I am not sure.

Answer & Explanation

Minbutastc

Minbutastc

Beginner2022-07-21Added 14 answers

Yes, you're correct: It doesn't matter. This is because, e.g., the probability that z=2.35 is exactly 0.
For a more formal proof, letting f be the appropriate pdf,
P ( z = 2.35 ) = 2.35 2.35 f ( x ) d x = 0
John Landry

John Landry

Beginner2022-07-22Added 3 answers

Note that you are misreading the table. We have Pr ( Z 2.35 ) 1 0.0094

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