# What does P(z>1.65) translate to probability

#### ocean1

##### New Member
Form the z table for standard normal curve, I am trying to find out the probability of z>1.65.

According to z table, z score of 1.65 is 0.4505

As such, can I say that the probablity of obtaining z value >1.65 is 0.4505?

Did I get it right?

#### Junes

##### Member
Form the z table for standard normal curve, I am trying to find out the probability of z>1.65.

According to z table, z score of 1.65 is 0.4505
Where did you get that number? The correct answer is 0.9505. EDIT: what I meant was that I thought this should be the number in the table. But see below.

As such, can I say that the probablity of obtaining z value >1.65 is 0.4505?

Did I get it right?
Even if 0.4505 were the right number, that wouldn't be quite correct. Could you tell me what you know about how to interpret a number in a z table?

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#### Dason

Form the z table for standard normal curve, I am trying to find out the probability of z>1.65.

According to z table, z score of 1.65 is 0.4505
Where did you get that number? The correct answer is 0.9505.
P(z < 1.65) is close to .9505 but P(z > 1.65) is definitely not .9505

My guess is that ocean1 is using a z table that gives you the area between 0 and your z score. Those are probably the least common type of z-table but I've seen them before.

Ocean1: Note that P(Z < 0) = .5 [Can you see what that needs to be true?] Use that along with what your table tells you [ P(0 < Z < 1.65) = .4505] can you figure out how to get P(Z > 1.65)?

#### Junes

##### Member
P(z < 1.65) is close to .9505 but P(z > 1.65) is definitely not .9505
Oops, phrased that a bit wrong there . What I meant was that .9505 should be the value in the z-table.

To be honest, I haven't seen a z-table in years, nor have any of my students I think (well, it's at the end of their books but I doubt they bother to look). It's TI-83s all the way...

#### Dason

To be honest, I haven't seen a z-table in years, nor have any of my students I think (well, it's at the end of their books but I doubt they bother to look). It's TI-83s all the way...
People still use TI-83s? Huh... alright.

#### Junes

##### Member
People still use TI-83s? Huh... alright.
The thing is, the use of a graphical calculator is now mandatory in high school level maths since about 12 years or so. So anyone who's taken maths from 15-16 on in a Dutch school in recent years (which is everyone at the higher levels, since some math, including basic statistics, is mandatory for everyone) has a TI-83 or similar (or newer models, but they seem quite similar to me). They're actually nice things to have on hand for quick calculations.

One problem is of course that some students have a pretty good grasp of how the thing works, but no idea what they're doing.

#### trinker

##### ggplot2orBust
here's how to use your z table:

1.65 is 0.4505 as you state. That means everything from the left of that line to the 50th percentile is 45.05% of the populations. In addition to that you have another 50% of the people below the 50th percentile. That's a total of 95.05% below this z score.
Your question was what is the probability of getting a score above this? So...
100-95.05=4.95% (.0495) which is what DancerTiffy gave you. It's good to remember how to do this because I now use a computer program to do all of these calculations for me.