Continuous Distribution problem.

Let U be a standard uniformly distributed random variable and N be a standard normally distributed random variable. Show that, for any :6, the random variable @_1(U + (1 U )(I'(U)) has the same distribution as N given N > 3:. Here (I) is the cumulative distribution function of the standard normal distribution and @'1 its inverse. (This fact can be exploited to simulate normal random variables conditioned to exceed some level :3)