Question

Given a mean of 61.2 and a standard deviation of 21.4, within how many standard deviations of the mean do the values 45,78,62,90, and 31 fall? a.0 b.1 c.2 d.3

Answer 1

Determine the number of standard deviations that needs to be subtracted from or added to the mean in order to arrive to the values given.

(1) 45 = 61.2 - 21.4n ; n = 0.757
(2) 78 = 61.2 + 21.4n ; n = 0.785
(3) 62 = 61.2 + 21.4n ; n = 0.037
(4) 90 = 61.2 + 21.4n ; n = 1.346
(5) 31 = 61.2 - 21.4n ; n = 1.4

Therefore, the answer for 45 and 78 is approximately 1 (letter b), for 62 is zero (letter a), and for the last two numbers, more than 1 or two (letter c).