The heights of 1000 students are approximately normally distributed with a mean of 174.5 centimeters and a standard deviation of 6.9 centimeters. Suppose 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,
b) the number of sample means that fall between 172.5 and 175.8 centimeters inclusive,