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Assume we are interested in looking at GRE scores of students admitted to graduate schools. Suppose GRE scores are Normally distributed with an average of 317 and a standard deviation of 11.5 points. Suppose we take a sample of 15 admitted students.
a. What is the probability that a randomly selected student will have a GRE score above 325?
b. What is the probability that a randomly selected student will have a GRE score under 312?
c. What is the probability that a randomly selected student will have a GRE score between 310 and 320?
d. What is the probability that the average GRE score from our sample of 15 students will be above 320?
e. What score defines the lowest 7.93% of the distribution for an individual student?
f. What score defines the highest 34.09% of the distribution for an individual student?
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