# Probability

• May 17th 2009, 06:39 PM
brumby_3
Probability
a) X ~ N(10, 0.25)
Find P(http://upload.wikimedia.org/math/6/0...a3cc6a1131.png > 10.25) where n = 10
Find x such that P(http://upload.wikimedia.org/math/6/0...a3cc6a1131.png > x) = 0.05 where n = 10

b) X ~ N(20.2, 4)
Find P(http://upload.wikimedia.org/math/6/0...a3cc6a1131.png < 19) where n = 20
Find x such that P(http://upload.wikimedia.org/math/6/0...a3cc6a1131.png < x) = 0.85 where n = 20

If someone could do a) as an example I should be able to do b. Also the http://upload.wikimedia.org/math/6/0...a3cc6a1131.png are supposed to be capital X's with the hat on top.

• May 17th 2009, 07:29 PM
matheagle
You need to standardize the sample mean.

$Z={\bar X-\mu\over \sigma/\sqrt n}\sim N(0,1)$

So, $P(\bar X >10.25)= P\biggl(Z> {10.25-10\over .5/\sqrt{10}}\biggr)$

Since $Z_{.05}=1.645$ the corresponding x value can be solved via $1.645={x-10\over .5/\sqrt {10}}$.
• May 17th 2009, 09:12 PM
hametceq
be cearful, if you are saying X ~ N(10, 0.25) =>
var=0.25 or sd=0.25 ???
some textbooks use format of X~N(mean, sd), anothers X~N(mean, var).

solution was provided by matheagle, assuming X~N(mean, var) format.