# Math Help - Standard normal

1. ## Standard normal

Work done so far....
If X ~ N(22,4), z = (x - 22)/sqrt(4) ~ N(0,1) Thus, P(20 <= X <= 21) = P((22-20)/2 <= z <= (22-21)/2) = P(1<= z <= 0.5) = P(z <= 1) - P(Z <= 0.5) Now, we use the table above. P(z <= 1) - P(Z <= 0.5) = 0.8413-0.6915=0.1463

Is it correct?

2. ## Re: Standard normal

Check your arithmetic at the very end, using numeric integration (assuming $\mu=22$ and $\sigma^2=4$ I'm not familiar with the notation given) I find:

$P(20

and using the table I have, I get 0.1498