Answer
(a) 86.64%
(b) 0.62%
(c) 0.04%
Work Step by Step
Suppose a certain population of observations is normally distributed. What percentage of the observations in the population
(a) are within ± 1.5 standard deviations of the mean?
Given
$-1.5 = 0.0668$
$+1.5 = 0.9332$
$0.9332 - 0.0668 = 0.8664 $
$0.8664 * 100 = 86.64%$
86.64%
(b) are more than 2.5 standard deviations above the mean?
Given
$+2.5 = 0.9938$
$1 - 0.9938 = 0.0062$
$0.0062 * 100 = 0.62%$
0.62%
(c) are more than 3.5 standard deviations away from (above or below) the mean?
Given
$-3.5 = 0.0002$
$+3.5 = 0.9998$
$0.9998 - 0.0002 = 0.9996$
$1 - 0.9996 = 0.0004$
$0.0004 * 100 = 0.04%$
0.04%
