1. ## Probability

a) X ~ N(10, 0.25)
Find P( > 10.25) where n = 10
Find x such that P( > x) = 0.05 where n = 10

b) X ~ N(20.2, 4)
Find P( < 19) where n = 20
Find x such that P( < x) = 0.85 where n = 20

If someone could do a) as an example I should be able to do b. Also the are supposed to be capital X's with the hat on top.

2. 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 $1.645={x-10\over .5/\sqrt {10}}$.

3. 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.