In: Statistics and Probability
For a certain standardized placement test, it was found that the scores were normally distributed, with a mean of 190 and a standard deviation of 30. Suppose that this test is given to 1000 students. (Recall that 34% of z-scores lie between 0 and 1, 13.5% lie between 1 and 2, and 2.5% are greater than 2.)
(a) How many are expected to make scores between 160 and 220?
(b) How many are expected to score above 250?
(c) What is the expected range of all the scores?