1. In N(100, 400), find:
a. The proportion of the values greater than 70
b. The values of y within the central 90% of the distribution
c. The smallest value of y that exceeds 85% of the distribution
d. The largest value of y that is below 60% of the distribution
2. Assume that Graduate Record Examination (GRE) scores follow a normal distribution with a mean of 1000 and a standard deviation of 200.
a. What percentage of graduates who take this exam have GRE scores greater than 750?
b. What GRE score separates the upper 30% of graduates from the other 70%?
c. Between what values are the scores of the central 90% of the graduates?
d. How likely is it that a randomly selected graduate will be one who has a GRE score greater than 1000? e. How likely is it that a random sample of 10 graduates will contain more than 7 who have GRE scores greater than 1000?
f. Suppose that a group of 10 graduates contains 8 who have GRE scores greater than 1000.
i. Does this appear to be a random sample?
ii. Why?