In the standard normal distribution, which of the following intervals between z scores contains the largest proportion of scores?
A)-1.0 to +1.0
B)0.0 to +1.0
C)+1.0 to +2.0
D)0.0 to -2.0

Question

Quizplus · Accepted Answer

The standard normal distribution is a bell-shaped curve with a mean of 0 and a standard deviation of 1. The z scores represent the number of standard deviations from the mean.

Interval A (-1.0 to +1.0) contains the mean of the distribution (0) and covers 68% of the area under the curve. This is the largest proportion of scores that can be contained within a single interval.

Interval B (0.0 to +1.0) covers only half of Interval A and contains 34% of the area under the curve.

Interval C (+1.0 to +2.0) and Interval D (0.0 to -2.0) both cover the same amount of area as Interval A, but they are split into two intervals each (1.0 to 2.0 and -2.0 to 0.0). Each of these smaller intervals contains only 14% of the area under the curve, which is less than Interval A.

Therefore, A) -1.0 to +1.0 contains the largest proportion of scores in the standard normal distribution.

In the Standard Normal Distribution, Which of the Following Intervals