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 = the average pH as determined by the morning students and = 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 ≤  - ≤ .1).
b. If there are 36 students in each lab, but pH determinations are not assumed normal, calculate (approximately) P(-.1 ≤  - ≤ .1).