Normal Sampling and Modelling
(using the Graphing Calculator)
Warm-Up
Recall the following definitions in statistics:
population:
all individuals or items that belong to a group being studied
eg. all of the students at OLMC
sample:
a group of items or people selected from a population
eg. the data management classes at OLMC
Different symbols are used to distinguish between the population (or actual) mean
and standard deviation values and the sample (or approximate) values.
population
sample
Mean
μ
x
Standard Deviation
σ
s
If a population is believed or expected to be normally distributed,
it may be modelled by a sample taken from that population.
Example 
Year
Return (%)
Year
Return (%)
a)
The annual returns from a particular mutual fund are believed to be
normally distributed. Erin is considering investing in this mutual fund.
She obtained a sample of 20 years of historic returns which are listed in
the table below.
1
7.2
11
6.4
2
12.3
12
27
3
17.1
13
14.5
4
17.9
14
25.2
5
10.8
15
-0.5
6
19.3
16
2.4
7
12.2
17
16.7
8
-13.1
18
12.8
9
20.2
19
2.9
10
18.6
20
18.8
Using a graphing calculator, determine the mean ( x ) and standard deviation
(s) of this data.
GRAPHING CALCULATOR RECALL:
Clear Lists:
Enter data:
Calculate:
2ND MEM 4:ClrAllLists
STAT EDIT Use L1
STAT CALC 1-Var Stats
b)
Assuming the data is normally distributed, determine the probability that
an annual return will be at least 9%.
c)
Use the graphing calculator to determine the above probability.
The cdf (cumulative density function) is used to calculate the probability
that a given data point lies between a lower and upper bound.
Note:
1 x 1099  
–1 x 1099  – 
GRAPHING CALCULATOR INSTRUCTIONS:
Use cdf: 2ND DISTR 2: normalcdf(
Normalcdf( lower bound, upper bound, mean, standard deviation )
Normalcdf( __________ , __________ , __________ , __________ )
 P(x > 9%) = ____________
d)
Use the graphing calculator to determine the probability that an annual
return will be negative.
Normalcdf( __________ , __________ , __________ , __________ )
 P(x < 0) = ____________