Probability of Exam Scores Based on Study Hours

A researcher examines the relationship between study hours and exam scores for a group of students. The study finds that the exam scores are normally distributed with a mean score of 75 and a standard deviation of 10. If a student studies for 8 hours per week, they are expected to score 85. Assume the relationship between hours studied and scores is linear within this range.

What is the probability that a randomly selected student, who studies 6 hours a week, scores higher than the expected score for that study duration? The expected score for 6 hours of study can be calculated by establishing a linear equation based on the points (6, x) and (8, 85), where x is the expected score for 6 hours.