Question

What are the percentages of scores that fall between:

a) -1 and 0/0 and 1

b) -1 and -2/1 and 2

c) In the tails of a normal distribution.

Answer 1

Empirical rule: For a normal distribution, 68% of values fall within 1 standard deviation of mean. 95% of values fall within 2 standard deviation of mean and 97.7% of values fall within 3 standard deviation of mean.

a)

That is 68% data values lies within one standard deviations of mean. That is percentage of data values lie between -1 and 0 is

68% /2 = 34%

That is percentage of data values lie between 0 and 1 is

68% /2 = 34%

b)

That is 95% data values lies within 2 standard deviations of mean. That is percentage of data values lie between -1 and 0 is

68% /2 = 34%

That is percentage of data values lie between -2 and 0 is

95% /2 = 47.5%

Percentage of data values lie between -2 and -1 is

47.5% - 34% = 13.5%

-------------------------

That is 95% data values lies within 2 standard deviations of mean. That is percentage of data values lie between 0 and 1 is

68% /2 = 34%

That is percentage of data values lie between 0 and 2 is

95% /2 = 47.5%

Percentage of data values lie between 1 and 2 is

47.5% - 34% = 13.5%

c)

The normal distribution is symmetric is about mean. That is area at left tail is 50% and area at right tail is 50%.