Question

Transforming a standard normal random variable to the general normal random variable with mean mu, and standard deviation sigma

Answer 1

guesssing it would be something like X ~ N[10,45] Find P(x<55)... something like that then you would do P[Z∗σ+μ < X < Z∗σ+μ] something like that?

Answer 2

if \(Z\sim N(0,1)\)

then \(X=\sigma Z+\mu\) has a normal distribution with mean \(\mu\) and sd \(\sigma\)

Answer 3

mean of 10, and sd of 45, i assume is the notation up there right?

Answer 4

to convert to the Z, if im reading it right, im never sure ....

N(10,45) needs to be modified to equate with N(0,1)

N(10-10,45/45) works, might not be kosher, but it works :)

so for any given X we have to subtract 10 and divide by 45 to equate it to Z