# Thread: normal distribution: > and <

1. ## normal distribution: > and <

How do you find P(X>111) and P(X<85) if the mean is 100 and the SD is 10? For the 1st one I did (111-100)/10=1.1 which is 0.1357 on the normal distribution table. For the 2nd one, I'm not so sure how to go about it. First I did (85-100)/10=-1.5. Since it is < rather than >, I just took the value of 1.5 from the normal distribution chart, 0.0668. Any suggestions? Thank you

How do you find P(X>111) and P(X<85) if the mean is 100 and the SD is 10? For the 1st one I did (111-100)/10=1.1 which is 0.1357 on the normal distribution table. For the 2nd one, I'm not so sure how to go about it. First I did (85-100)/10=-1.5. Since it is < rather than >, I just took the value of 1.5 from the normal distribution chart, 0.0668. Any suggestions? Thank you

$\displaystyle P(Z<-1.5)=P(Z>1.5)$ by symmetry.
This is a very nice stat calculator...
http://www.danielsoper.com/statcalc/calc20.aspx
Plug in 1.5 and you get $\displaystyle P(Z<-1.5)=P(Z>1.5)=.0668072$

3. great calculator! those were the answers i had actually handed in and they were incorrect.... so i figured i went wrong somewhere.

NOW, I'm confused.

5. Originally Posted by matheagle
NOW, I'm confused.
The correct (to seven decimal places) answer to P(X < 85) is indeed 0.0668072.

So either:

1. Whoever graded the work has made a mistake (possibly a TA working off a wrong answer sheet)

2. The answer is 'too correct' ....

6. and I'm too tired, gn.

great calculator! those were the answers i had actually handed in and they were incorrect.... so i figured i went wrong somewhere.
Quote what you are responding to, that way your post just might make sense. As it is you leave us guessing what you handed in and had marked as wrong (use the 'quote' button below and to the right of the post you are looking at).

CB

8. Originally Posted by mr fantastic
The correct (to seven decimal places) answer to P(X < 85) is indeed 0.0668072.

So either:

1. Whoever graded the work has made a mistake (possibly a TA working off a wrong answer sheet)

2. The answer is 'too correct' ....
You are making an assumption about which post madgab was responding to which may not be valid.

CB