TIMSS 2003 (Trends in International Mathematics and Science Study) focused on the mathematics and science achievement of eighth-graders throughout the world. A total of 45 countries (including the United States) participated in the study. The mean math exam score for U.S. students was 504 with a standard deviation of 88.

Source: http://nces.ed.gov/timss/TIMSS03Tables Assume the scores are normally distributed and a sample of 150 students is taken.

a. Find the probability that the mean TIMSS score for a randomly selected group of eighthgraders would be between 495 and 510.

b. Find the probability that the mean TIMSS score for a randomly selected group of eighthgraders would be less than 520.

c. Do you think the assumption of normality is reasonable? Explain.