MSM 709

TI-83/84 commands for Ch. 6, 7

 

To find values from the Normal Distribution:

            1.  If you know an interval and are looking for area (percentage), use 2nd DISTR 2:normalcdf  and hit ENTER.  This pastes it onto the home screen.  You must then enter as follows:

 

            Normalcdf(lowerbound,upperbound,μ,σ)  then hit ENTER

 

            Remember that μ is the mean of the normal distribution and σ is its standard deviation.

 

2.      If you know the area and are looking for values along the horizontal (i.e. percentiles) use 2nd DISTR 3:invNorm and hit ENTER.  This pastes it to the home screen.  You must then enter as follows:

 

            InvNorm(Area to the left of the value you have,μ,σ)  then hit ENTER.

 

Generating random numbers / Simulations

 

Random numbers can be used for:

1.                  Selecting a random sample from a population in which the members of the population are numbered.

2.                  Simulations to estimate the probability of events. 

 

Before you attempt to generate random numbers on the TI-83 you must first set the “seed number” as follows: Use the last four digits of your Social Security number.  Key in the number, select STO>MATH PRB 1:rand ENTER.  The starting point for generating random numbers has now been set.

 

Generating random integers on the TI-83:

 

Ex. 1: Generate a list of 5 random whole numbers between 1 and 50.  Select MATH PRB 5:randInt( ENTER.  Since we want the integers to fall between 1 and 50, enter

 

                        RandInt(1,50) ENTER.  Press ENTER 5 times to generate the 5 numbers.  If a number is repeated, discard it and press ENTER again to get a different random number.

 

 

Ex. 2: Scientists estimate that experimental rockets currently produced by NASA have an 80% success rate on launch.  Use a simulation to estimate the number of launches until you see a launch fail.

 

Ex. 3: Use simulations to estimate the probability that it will take you more than 4 flips of a coin to come up with three heads.

 

Generating random observations from a normal model:

Select MATH PRB 6:randNorm( ENTER.  Then enter the mean and standard deviation , and hit ENTER to generate the number.

 

Ex. 1: Generate 5 random observations from a normal model with a mean of 54 and a standard deviation of 7.

                        MATH PRB 6:randNorm( ENTER

Then enter       randNorm(54,7) and hit ENTER 5 times to generate the five numbers.

 

Ex 2: Applicants to a certain college have math SAT scores that follow a normal model with a mean of 510 and a standard deviation of 106.  An admissions officer selects applications at random.  Run a simulation to estimate the number of applications he will have to look at before finding three with a math SAT score of over 600.