Question about z scores

Question

For each of the following populations, would a score of 85 be considered central (near the mean) or in the extremes (closer to the tails)?

a. mean = 75 and SD = 15

b. mean = 80 and SD = 2

c. mean = 90 and SD = 20

d. mean = 93 and SD = 3

Answer 1

calculates the z-scores

z = (x-mean)/stddev

Anything in the interval (-1,1) is close

to the mean

(a) (85-75)/15 = 10/15 = 2/3 < 1 YES

(b) (85-80)/2 = 5/2 = 2.5 > 1 NO

(c) (85-90)/20 = -5/20 = -0.25 > -1 YEs

(d) (85-93)/3 = -8/3 = -2.6666... < -1 NO