Reconsider Exercise 11.8.22, but with different sample sizes. Determine the probability that Karen grades a random sample of five exams in less total time than it takes John to grade a random sample of four exams. First express this event in terms of  (x̅_Karen − x̅_John), keeping in mind the different sample sizes for the two graders.

Data from Exercise 11.8.22

Suppose that Karen and John get together to grade their students’ exams. The time required for Karen to grade a question on a student’s exam is normally distributed with mean 90 seconds and standard deviation 20 seconds. The time required for John to grade a question on a student’s exam follows a normal distribution with mean 120 seconds and standard deviation 30 seconds. Suppose that each person grades a random sample of 10 questions on their students’ exams.