This is from an old PhD exam:

Given $\displaystyle X_1, X_2, \ldots , X_n $ are i.i.d. to $\displaystyle N( \mu , 1 ) $

And define $\displaystyle Y_i = I \{ X_i < 0 \} $

Then $\displaystyle Y_1, Y_2, \ldots , Y_n $ are i.i.d. to $\displaystyle Bernoulli(p)$ where $\displaystyle p = Pr (X<0) = \Phi (- \mu ) $

Now, my question really is... Why is $\displaystyle Pr (X<0) = \Phi (- \mu ) $?

Thank you!