1. ## Normal distribution

Hey guys, was wondering if you guys could help me out with this, been ok so far with my Stats at Uni but not sure what to do with these examples, can anyone help me or just give me the formula I'm meant to use for each? Need to do this by tomorrow morning, only reason I'm posting in this section.

a) Random Variable X has N(2,3) distribution
i) Evauluate P (X>3)
ii) P(-1<X<4)
iii) Find a such that P([X-2]<a)=0.1

b) X and Y are now independent with N(1,5) and N(5,1)
i) Evauluate P(X<0, y>6)
ii) P(-3<3X - Y<0)

2. Originally Posted by Mathsnewbie
Hey guys, was wondering if you guys could help me out with this, been ok so far with my Stats at Uni but not sure what to do with these examples, can anyone help me or just give me the formula I'm meant to use for each? Need to do this by tomorrow morning, only reason I'm posting in this section.

a) Random Variable X has N(2,3) distribution
i) Evauluate P (X>3)
ii) P(-1<X<4)

Mr F says: In each case you convert the value of X to a z-value using the formula $\displaystyle {\color{red}Z = \frac{X - \mu}{\sigma}}$. Then use your Four-Figure Standard Normal Distribution Tables. Is 3 the variance or the standard deviation of X?

iii) Find a such that P([X-2]<a)=0.1

Mr F says: What does [X-2] mean .... Do you mean |X-2|? In any case, use your standard normal tables in reverse.

b) X and Y are now independent with N(1,5) and N(5,1)
i) Evauluate P(X<0, y>6)

Mr F says: Calculate $\displaystyle {\color{red}\Pr(X < 0) \cdot \Pr(Y > 6)}$.

ii) P(-3<3X - Y<0)
ii) You need to integrate the joint pdf over the region of the XY-plane defined by $\displaystyle -3 < 3X - Y < 0 \Rightarrow 3X < Y < 3x + 3$.