In a recent year grade 8 Washington State public school students taking a mathematics assessment test had a mean score of 276.1 with a standard deviation of 34.4. Possible test scores could range from 0 to 500. Assume that the scores are normally distributed.
a) Find the probability that a student had a score higher than 325?
b) Find the probability that a student had a score between 250 and 305?
c) What percentage of the students had a test score that is greater than 250?
d) If 2000 students are randomly selected, how many will have a test score that is less than 300?
e) What is the lowest score that would place a student in the top 5% of the scores?
f) What is the highest score that would place a student in the bottom 25% of the scores?
g) A random sample of 60 students is drawn from this population. What is the probability that the mean test score is greater than 300?