34. 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 normally distributed random variable and there are 25 students in each lab, compute

. (Hint: is a linear combination of normal variables, so it is normally distributed. Compute mXY and sXY .)

P1.1 X  Y

.12 X  Y Y

X

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

.