SAT Scores The SAT is an exam used by colleges and universit

SAT Scores The SAT is an exam used by colleges and universities to evalute undergraduate applicants. The test scores are normally distributed. In a recent year, the mean test score was 1498 and the standard deviation was 316. The test scores of four students selected at random are 1920, 1240, 2200, and 1390.( a) find the z-scores that corresponds to each value and (b) determine whether any of the values are unusal.

Solution

a)

Note that x = (x- u )/sigma.

Hence, for x = 1920:

z = (1920 - 1498)/316 = 1.335443038 [ANSWER]

Hence, for x = 1240:

z = (1240 - 1498)/316 = -0.816455696 [ANSWER]

Hence, for x = 2200:

z = (2200 - 1498)/316 = 2.221518987 [ANSWER]

Hence, for x = 1390:

z = (1390 - 1498)/316 = -0.341772152 [ANSWER]

***********************

b)

Only x = 2200 is unusual, as |z| > 2. [ANSWER]