Finding an unknown value in normal distribution.

• Mar 12th 2010, 01:23 PM
CSG18
Finding an unknown value in normal distribution.
The continuous random variable Y is normally distributed with mean 15 and standard deviation 6
(a) Find P(X21)

(b) Find the value of d such that P(15<X<d)=0.3152

How do you answer part (b)?
• Mar 12th 2010, 01:27 PM
mr fantastic
Quote:

Originally Posted by CSG18
The continuous random variable Y is normally distributed with mean 15 and standard deviation 6
(a) Find P(X21)

(b) Find the value of d such that P(15<X<d)=0.3152

How do you answer part (b)?

Note that the mean is 15. So you have:

Pr(X < d) - 0.5 = 0.3152 => Pr(X < d) = 0.8152. This is now a simple inverse normal problem.
• Mar 12th 2010, 01:32 PM
CSG18
I do not understand where 0.5 comes from. Could you explain please? Also how would you reach the final answer..I guess I do not know how to solve a simple inverse normal problem..

Thanks!
• Mar 12th 2010, 01:34 PM
mr fantastic
Quote:

Originally Posted by CSG18
I do not understand where 0.5 comes from. Could you explain please?

Thanks!

Are you aware that Pr(X < mean) = 0.5 for a normal distribution?

Quote:

Originally Posted by CSG18
[snip from edited reply] Also how would you reach the final answer..I guess I do not know how to solve a simple inverse normal problem..

Thanks!

Your textbook and class notes should have examples of how to do that. Have you reviewed that material?
• Mar 12th 2010, 01:49 PM
CSG18
Well our teacher has not taught us normal distribution, so I have to learn it by myself. It's ok I'll figure it out.

Thanks
• Mar 12th 2010, 01:52 PM
mr fantastic
Quote:

Originally Posted by CSG18
Well our teacher has not taught us normal distribution, so I have to learn it by myself. It's ok I'll figure it out.

Thanks

Fnd the value z* of Z such that Pr(Z < z*) = 0.8152. Then z* = (d - 15)/6. Solve for d.

By the way, why are you attempting questions that your teacher has not taught you how to do?
• Mar 12th 2010, 01:59 PM
CSG18
It's going to be on my exam, but I don't think my teacher will have time to teach us it. So I will have to learn it.

Thanks I get it now!
• Mar 12th 2010, 02:22 PM
mr fantastic
Quote:

Originally Posted by CSG18
It's going to be on my exam, but I don't think my teacher will have time to teach us it. So I will have to learn it.

The only thing I don't understand is how to get z*. How does 0.8152 get to 0.897?

How can an exam possbly test you on material that has not been taught? Unfortunately, there are many things the question you posted expects you to already understand. MHF cannot act as a surrogate teacher. If you have resolved to self-learn the normal distribution I suggest you obtain a decent textbook that covers the material and start from the very beginning.

I also suggest you discuss the issues raised in this thread with your teacher.
• Mar 12th 2010, 04:56 PM
CSG18
I understand, thanks for your help. I'm doing the IB and in my first year my original maths teacher was supposed to teach my class normal distribution but didn't, so now my new teacher probably won't have time to teach it.
• Mar 12th 2010, 09:45 PM
mr fantastic
Quote:

Originally Posted by CSG18
I understand, thanks for your help. I'm doing the IB and in my first year my original maths teacher was supposed to teach my class normal distribution but didn't, so now my new teacher probably won't have time to teach it.