Download TI-83 Worksheet Number 23

WS #23 Normal Distributions
Solving Problems with the Add-in Program NORMDIST
Problem: Given a normal distribution for Scholastic Aptitude Test (SAT) is N(500, 100),
that is, the mean is 500 and the standard deviation is 100. What is the probability a student
scored between 400 and 650?
Key Strokes
PGRM
Display/Comment
Brings up the Add-in Program Menu
3 ENTER
Shows the option for two types of problems.
We will select 1 because our problem gives us
the interval (400, 600) and asks for the % of
individual students in that interval.
1 ENTER
The program asks for the lower bound of the
interval which is 400.
400 ENTER
The program asks for the upper bound of the
interval which is 650.
650 ENTER
The program now asks for the mean of the
normal distribution which is 500.
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500 ENTER
The program now asks for the Standard
Deviation of the normal distribution which or
the Standard error of the sampling distribution.
Since this is a population distribution, the
proper entry is 100.
100 ENTER
The program gives the answer: The probability
the student scored between 400 and 650 is
0.7745%
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Problem: Given a normal distribution for Scholastic Aptitude Test (SAT) is N(500, 100),
that is, the mean is 500 and the standard deviation is 100. What percent of individuals
scored less than 300?
Key Strokes
PRGM 3 ENTER
Display/Comment
The interval we are looking for is (-  , 300).
Since the calculator does not have the
 symbol, we have to use the smallest number
in the calculator which is  1 10 99 or -E99.
The calculator interval is (-E99, 300). We
select 1.
1 ENTER
- 2ND EE 99 ENTER
300 ENTER
500 ENTER
100 ENTER
The probability a student scored less than 300
is .0228.
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Problem: Given a normal distribution for Scholastic Aptitude Test (SAT) is N(500, 100),
that is the mean is 500 and the standard deviation is 100. What score would it take to be in
the in the top 10% of all students.
Key Strokes
PGRM 3 ENTER
Display/Comment
The top 10% is the rightmost 10% area.. We
are given an area, and we need to find the right
bound on the x-axis We select 2.
2 ENTER
The area from the left is 100-.10 = 0.90
0.90 ENTER
500 ENTER
100 ENTER
The score required is 628.1552. Any score
above this number will be in the top 10% of
all scores.
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Solving Problems with the TI-38 built in programs: NORMALCDF and INVNORMAL
Problem: Given a normal distribution for Scholastic Aptitude Test (SAT) is N(500, 100),
that is, the mean is 500 and the standard deviation is 100. What percent of students had
scores less that 750.
When we know the interval (, 750) and want the area above it, we use the Normalcdf
command. This command takes the form of Normalcdf (lower bound, upper bound, mean,
standard deviation).
The TI-83 has no symbol or negative or positive infinity,   or   , so we use  10 99 for
negative infinity and 10 99 for positive infinity. These are the smallest and largest numbers
the TI 83 will take.
Key Strokes
nd
Comment
2 DISTR
Displays the
Distribution
Menu
2 Enter
Displays the
normalcdf on the
home page
Enters the
parameters for the
command
- 2nd EE 99 , 750 , 500, 100 )
Enter
Displays the answer 0.9938. This means that
99.38% of the test scores are lower than 750.
Problem: Given the SAT distribution of N(500, 100), what score would it take to get into
the top 10% of all tests.
To be in the top 4% of the tests would require a score above the 96th percentile.
For this problem, we use the invNoraml command. This command takes the form
invNormal (percentile, mean, standard deviation).
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Key Strokes
Comment
nd
2 Distr 3
0.96 , 500, 100, )
Enter
Add the proper parameters to the command
Display :
A test score of
675.069 will be above 96 percent of all tests
taken and in the top 4% of all tests.
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