
Computing Probability
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 0.2. A large bath 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 the probability P(0.1 < XY < 0.1)
Hint: XY is a linear combination of normal variables, so is normally distributed with mean E(XY) = E(X)E(Y) and variance V(XY) = V(X)+V(Y)
b.) If there are 36 students in each lab, but pH determinations are not assumed normal, calculate (approximately) P(0.1 < XY < 0.1)
*X and Y are X bar and Y bar. I just cannot place bars above letter so that's the best I can do
I don't really want the answer given to me, but I honestly don't really understand the data that they are giving me because of how it is said. So perhaps if someone could break that down and give me a few of the basic overall steps that I need to do that would help me a ton!