# Standardising

How do I find z?
(edited 1 year ago)
Try to get in the habit of writing down all the info in the question.
Here you'd use the 5% info to get an equation to get sigma, then use sigma to get the 1.05 probability.
Original post by mqb2766
Try to get in the habit of writing down all the info in the question.
Here you'd use the 5% info to get an equation to get sigma, then use sigma to get the 1.05 probability.

What are they doing next to find the probability?
P(x>1.05) = 1 - P(x<=1.05)
Its just the usual stuff?
They're using the Z-table. Once you know how many $\sigma$ from the mean the value is, that's all you need to work out probability.
Original post by mqb2766
P(x>1.05) = 1 - P(x<=1.05)
Its just the usual stuff?

What are the value for mu and sigma that I would put in because I’m not getting anything close to them?
Original post by Bigflakes
What are the value for mu and sigma that I would put in because I’m not getting anything close to them?

sigma 0.0182 should be from the first part and mu is given in the question 1.03.
The difference of 0.02 (1.05-1.03) is about 1 standard deviation, so the upper tail shoulld be about 15% which is what the answer is. Upload what youve tried if youre still unsure.
(edited 1 year ago)
Original post by mqb2766
sigma 0.0182 should be from the first part and mu is given in the question 1.03.
The difference of 0.02 (1.05-1.03) is about 1 standard deviation, so the upper tail shoulld be about 15% which is what the answer is. Upload what youve tried if youre still unsure.

It’s just my calculator, my lower bound is 1.05, my upper bound is a big number and my mu/sigma are what you said but that gets me a p of 0.46
Original post by Sinnoh
They're using the Z-table. Once you know how many $\sigma$ from the mean the value is, that's all you need to work out probability.

So it’s 1.09 sigma away from the mean but how would I change that into a probability?
(edited 1 year ago)
Original post by Bigflakes
It’s just my calculator, my lower bound is 1.05, my upper bound is a big number and my mu/sigma are what you said but that gets me a p of 0.46

2 is a big number in this context, can you try it with that?
Original post by Bigflakes
So it’s 1.09 sigma away from the mean but how would I change that into a probability?

That is your z value, 1.09. So calculator/tables to get the cumulative probability for eitehr
P(z<=1.09)
P(z>=1.09)
(edited 1 year ago)
Original post by mqb2766
2 is a big number in this context, can you try it with that?

It still gives me 0.45, but also when I graph it, it’s not using 1.05 as the lower bound even though I put it in?
z should be 1.09, not 0.109?
z uppper should be ~10
Original post by mqb2766
That is your z value, 1.09. So calculator/tables to get the cumulative probability for eitehr
P(z<=1.09)
P(z>=1.09)

Yeah so when I use 1.09 as lower, mu as 0 and sigma as 1 it gives me the correct answer
Original post by Bigflakes
Yeah so when I use 1.09 as lower, mu as 0 and sigma as 1 it gives me the correct answer

Did you enter 0.0182 or 0.182 for sigma?
Original post by mqb2766
z should be 1.09, not 0.109?
z uppper should be ~10

So what should I put in as the bounds of I’m using mu as 1.03 and sigma as 0.0183
Original post by Bigflakes
So what should I put in as the bounds of I’m using mu as 1.03 and sigma as 0.0183

Lower bound 1.05
Upper bound 1.5
Sometimes you can run into numerical errors if the upper bound is way too large. Something a bit greater than 10 std devs (so around 0.2 here) would be more than sufficient
Original post by mqb2766
Did you enter 0.0182 or 0.182 for sigma?

Yeah I think that’s what was wrong I’ve got it now, thank you