Normal distributions

Question

About _% of the area under the curve of the standard normal distribution is outside the interval z=[-1.68,1.68] (or beyond 1.68 standard deviations of the mean.)

Answer 1

.092957 = 9.2957% outside the + and - z scores

use a z calculator, z tables or a stat program

do a check with the empirical rule

to see if you're in the right range

95% is within 2 standard deviations of the mean

100-95= 5 outside 2 standard deviations

1.68 is less than 2, so expect more than 5%

the empirical rule has 68% within 1 standard deviation, leavung 68/2 = 34% outside

5 < 9.3 < 34, 1<1.68< 2

that use of 68 and 1.68 might trip up some people. they're unrelated