Suppose that when the pH of a certain chemical compound is 5.00, the pH measured by a randomly selected beginning chemistry student is a random variable with mean 5.00 and standard deviation .2. A large batch of the compound 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 students and Y
the average pH as determined by the afternoon students.

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

Y and X

Y

.]

b. If there are 36 students in each lab, but pH determinations are not assumed normal, calculate (approximately)

P(.1  X  Y  .1).