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 aver- age pH as determined by the morning students and Y = the average pH as determined by the afternoon students. a. If pH is a normally distributed random 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 it is normally distributed.
b. If there are 36 students in each lab, but pH deter- minations are not assumed normal, calculate (ap- proximately)
P(-.1≤ X - Y ≤.1).