Question

essearchers measure the political afiliation of students (higher scores indicate a more liberal p liation). They find that the mean score on the scale is 17.00 and the standard deviation is 2.25. Use this information to 1) find the Z score for the individuals below, 2) find the percent between the mean and the Z, the percent above, and the percent below each Z score, and 3) select three of the Z scores and interpret the meaning of the scores. X-M % Between 1 %) Below Z | % Above Z M and Z 26 21 19 24 17 28

Answer 1

X	X-M	Z	% between M and Z	% below Z	% above Z
26	9	4	49.9968	99.9936	0.0064
21	4	1.777778	46.53	96.23	3.77
19	2	0.888889	31.3	81.3	18.7
24	7	3.111111	49.91	99.9991	0.0009
17	0	0	0	50	50
28	11	4.888889	50	100	0

increase Z score means increase standard deviation from the mean.

Z Score means there is no difference between the sample mean and population mean so the standard deviation is zero.

Z score 4 means 4 standard deviations from mean so, the sample deviates from the population mean and 0.88889 means 0.88889 standard deviations from mean