Worksheet 4-2:

For the standard normal distribution, 15.87% of values are less than -1, 34.13% of values are less than

zero but at least -1, 34.13% of values are less than +1 but at least zero, and 15.87% of values are at least

+1.

Looking at standardized scores for total annual returns on the S&P 500 from 1928 through 2021, there

were 18 years with a standardized score less than -1, 24 years with a standardized score less than zero

but at least -1, 36 years with a standardized score at least zero but less than +1, and 16 years with a

standardized score at least +1.

Using a 0.10 significance level, what do the above counts indicate about whether total annual returns on

the S&P 500 are normally distributed?