User Guide –

Statistics and Probability Made Easy

 

 

Topic

Description

Correct

Incorrect

 

1)        General usage of the TI89/Voyage200

a) Multiplication of variables

b) Enter .5 instead of ˝ to obtain decimal answers.

c) Roots: i.e. 3√x

d) Denominators

e) Squaring sin(x)

f) Attention to parentheses:

g) Euler Number

h) Parentheses

x*y^2,  x*cos(x)

 

use ˝*x or .5*x 

 

 

x^(1/3)

1/(x-2)

sin(x)^2

I.e. ln(sin(5x))/(x^2-1)

e (using Diamond e^x)

(x^2-9)/(3+x^2) 

xy^2,  xcos(x)

 

 

 

 

3√x

1/x-2

sin(x^2)

 


e (Alpha e)

(x^2-9)/3+x^2 

 

2)        General usage of SPME

a) Use ESC to exit the current module or SPME altogether.

b) Incorrect Entries – see above - yield the error message: “Invalid Entry”. Press ENTER and correct expression.

c) To force decimal answers, use decimal input (see also 1b)     

d) Provide 140,000 of RAM and 180,000 of Flash ROM (to check:2nd 6). Deleting or archiving files may be necessary: use 2nd “–“ (VAR-LINK), F4 to select files, then F1 to delete or archive. Archiving might be a good way to manage programs, variables, etc as a loss of battery power may delete any unarchived files. 

e) Emptying the MAIN folder when starting SPME will prevent any file reoccurrences (and thus loading error).

f) Should SPME not start (anymore) or act strange, reset ALL memory (2nd 6, then F1) as memory may be corrupted. 

g) Use the latest Operating System (OS) using TI Connect. 

 

 

 

3)        Garbage Collection

 

Nothing to worry about. The calculator reorganizes memory for proper functioning of APPS such as SPME. 

 

 

 

4)        Incorrect Program Termination.

If SPME is not properly terminated using ESC, these two error messages may occur. Simply press ESC (up to 50 times) , then restart SPME. If trouble persists: take out all 4+1 batteries and reinstall SPME. 

 

 

5)

Correct:

1) L1= {1,2,3}
2) L1= {1,2,4.3,9.1}

Note: Assure to use { } and , to separate numbers.

Incorrect:

1) L1= (1,2,3)
2) L1= [1,2,3]
Note: Assure to use { } and !! 

 

6)

Correct:

1) L1= {1,2,3}
2) L2= {1,2,4.3}

Note: Assure that list lengths match. (Exception: Non-Parametric Tests.)  Assure to use { } and , to separate numbers.

Incorrect:

1) L1= {1,2,3}
2) L2= {1,2,5,4.3}
Note: L2 hast 1 more entry !! 

 

 

 

 

 

 

 

 

Below find sample solutions to Normal Distribution problems:

 


 

Find the z-score for which the area under the standard normal curve to its left is 0.40

 

 

SELECT P(X<b)

mean=0

sigma=1

b= -.25

 

VOILA.

 

 

Response

Value

Correct Answer

0.25

 

 

Student Response 

-0.25

100%

Student Response  

-0.57

 

 

0.57

 

 

Score:

10/10

 

Find the specified area under the standard normal curve.

The area that lies between 0 and 3.01

 

 

SELECT P(a<X<b)

mean=0

sigma=1

a=0

b=3.01

 

 

Response

Value

Correct Answer

0.1217

 

 

0.5013

 

 

0.9987

 

 

Student Response 

0.4987

100%

Student Response  

Score:

10/10

Find the indicated probability or percentage for the normally distributed variable.

Assume that the weights of quarters are normally distributed with a mean of 5.67 g and a

standard deviation 0.070 g. A vending machine will only accept coins weighing

between 5.48 g and 5.82 g. What percentage of legal quarters will be rejected?

 

 

SELECT P(a<X<b)

mean=5.67

sigma=0.07

a=5.48

b=5.82

 

subtract that from 100% because rejected!

 

 

Response

Value

Correct Answer

1.62%

 

 

2.48%

 

 

Student Response 

1.96%

100%

Student Response  

0.0196%

 

 

Score:

10/10

 

 

The lifetimes of lightbulbs of a particular type are normally distributed with a mean of 266 hours and a standard deviation of 9 hours. Find the first quartile, Q1.

 

 

SELECT P(X<b)

mean=266

sigma=9

b=259.97

 

 

 Response

Value

Correct Answer

263.75

 

 

272.03

 

 

268.25

 

 

Student Response 

259.97

100%

Student Response  

Score:

10/10

 

Find the specified percentile, quartile, or decile.

Scores on an English test are normally distributed with a mean of 34.9 and a standard deviation

 of 6.7. Find the 41st percentile.

 

 

SELECT P(X<b)

mean=34.9

sigma=6.7

b=33.4 

 

 

 

Response

Value

Correct Answer

Student Response 

33.4

100%

Student Response  

30.9

 

 

36.4

 

 

38.9

 

 

Score:

10/10

 

Find the indicated probability or percentage for the sampling error.

The distribution of weekly salaries at a large company is right skewed with a mean of $1000 and

a standard deviation of $350. What is the probability that the sampling error made in estimating

the mean weekly salary for all employees of the company by the mean of a random sample of

weekly salaries of 50 employees will be at most $50?

 

SELECT P(a<X<b)

mean=1000

sigma=350/sqrt(50)    using the sampling distribution

a=950

b=1050

ENTER.

 

 

Response

Value

Correct Answer

0.3124

 

 

Student Response 

0.6876

100%

Student Response  

0.3438

 

 

Cannot be determined, because the distribution of the population is not normal.