MTH 203 Point Loma Nazarene University Normal Distribution Lab Report
Question Description
Lab 4: Normal Distributions
Instructions: Answer each of the following questions in a word document.
Goals: The purpose of this lab is to look at how well the rules about probabilities apply to data
that is approximately Normally distributed. You will be doing some calculations using the
Normal distribution table and then comparing those results to what you get when you actually
count the percent of data falling in each range.
The data for this lab consists of the S & P 500’s annual rate of return from 1986 to 2019. It is
often used as an assessment of overall returns on the stock market.
1. Download the data StockMarketReturns and generate a histogram and the mean and
standard deviation for the Return variable.
2. How close is this data to Normal? Explain what you see and how it compares to Normal.
3. Assuming this data is close enough to Normal to make reasonable approximations, use
the Normal distribution table and the mean and standard deviations you just computed to
find each of the following:
a. The percent of years with a return less than 0.3.
b. The percent of years with a negative return.
c. The percent of years with a return over 10%.
d. The percent of years with a return between 0.10 and 0.20.
e. What return is higher than 75% of all annual returns?
4. Now we would like to see if you were to actually count to find the percent of data
matching each of these criteria, and then compare to see how close the estimates are.
You may do this manually by just counting the data by inspection. There are 34 years
total. Alternatively, you can use software to help out. In order to obtain the percent of
years with a return over 0.05, you can sort the returns by selecting column B and then
sort using the Sort and Filter button on the Home menu. Chose to sort from smallest to
largest. You will be asked to expand or continue with the current selection. As long as
you have nothing in Column C, go ahead and expand (in this case, the Year will stay with
the Return value). This will make counting far easier. You can also use the command
=PERCENTILE(B:B,0.75) to find the cut point between the Return values at the 75th
percentile.
a. The actual percent of years with a return less than 0.3.
b. The actual percent of years with a negative return.
c. The actual percent of years with a return over 10%.
d. The actual percent of years with a return between 0.10 and 0.20.
e. What return is actually higher than 75% of all annual returns?
