Given X~N(21,4)

Question

(a) Find the z-score for 𝑥 = 26.

(b) Would 𝑥 = 10 be considered usual, unusual, or very unusual?

Answer 1

Mean is 21, standard deviation is 4

z-score = (x-mean)/standard deviation

z-score = (26 - 21)/4 = 1.25

z-score for x = 10 = (10-21)/4 = -2.75

Per standard normal probabilities table there is only a 0.0030 probability of getting a value as extreme as x=10 given N(21,4) which makes that value very unusual.