Suppose that when the pH of a certain chemical compound is 5.00, the pH measured by a randomly selected begin- ning chemistry student is a random variable with mean 5.00 and standard deviation .2. A large batch of the com- pound is subdivided and a sample given to each student in a morning lab and each student in an afternoon lab. Let X the average pH as determined by the morning stu- dents and Y = the average pH as determined by the after- noon students.

a. If pH is a normal variable and there are 25 students in each lab, compute P(-1-Ys.1). [Hint: X- Yis a linear combination of normal variables, so is normally distributed. Compute and ] x-

b. If there are 36 students in each lab, but pH determina- tions are not assumed normal, calculate (approximately) P(-.1 X-Y.1).