Empirical research on stock market data indicates that over the course of a year, 50% of stocks go up. A random sample of 400 stocks is going to be chosen at the beginning of next year. Let P be the proportion of the stocks in the sample that go up over the course of a year. Find the mean of P. Find the standard deviation of P.

Compute an approximation for P (p > 0.52), which is the probability that more than 52% of the stocks in the sample go up over the course of the year. Round you answer to four decimal places.