how to know if population is normally distributed
Thus based on the data in the sample an sich (as calculated by a test for normality), it is unlikely that the sample is part of a normal distribution, but we already know it is part of a normal distribution, because it's part of population that is normally distributed.
The mean of the sampling distribution will be equal to the mean of the population distribution. In the population, half of the births result in boys; and half, in girls. Therefore, the probability of boy births in the population is 0.50. Thus, the mean proportion in the sampling distribution should also be 0.50.