Question

A standardized​ exam's scores are normally distributed. In a recent​ year, the mean test score was 1548 and the standard deviation was 319. The test scores of four students selected at random are 1990​, 1280​, 2240​, and 1450. Find the​ z-scores that correspond to each value and determine whether any of the values are unusual.

Answer 1

Step-by-step explanation:

z-score is:

z = (x − μ) / σ

For the four students:

z = (1990 − 1548) / 319 = 1.39

z = (1280 − 1548) / 319 = -0.84

z = (2240 − 1548) / 319 = 2.17

z = (1450 − 1548) / 319 = -0.31

z-scores are considered significant if they are less than -2 or greater than 2.  So the third student's score is unusual.