The heights of 1000 students are approximately normally distributed with a mean of 174.5 centimeters and a standard deviation of 6.9 centimeters. If 200 random samples of size 25 are drawn from this population and the means recorded to the nearest tenth of a centimeter, determine
(a) The mean and standard deviation of the sampling distribution of X;
(b) The number of sample means that fall between 172.5 and 175.8 centimeters inclusive;
(c) The number of sample means falling below 172.0 centimeters.