1 Using calculator TI-83/84 1. Enter values into L1 list: press “stat” 2. Calculate all statistics: press “stat”

2 Binomial Probability Formula P(x) = p x q n-x n !n ! ( n – x )! x ! Number of outcomes with exactly x successes among n trials The probability of x successes among n trials for any one particular order

3 Using TI-83/84 Press 2 nd VARS to get the DISTR menu Scroll down to binomialpdf( and press ENTER Type in three values: n, p, x (separated by commas) and close the parenthesis You see a line like binomialpdf(10,.3,6) Press ENTER and read the probability of the value x (successes) in n trials

4 Alternative use of TI-83/84 Press 2 nd VARS to get the DISTR menu Scroll down to binomialcdf( and press ENTER Type in three values: n, p, x (separated by commas) and close the parenthesis You see a line like binomialcdf(10,.3,6) Press ENTER and read the combined probability of all values from 0 to x (i.e., probability that there are at most x successes)

5 Mean, Variance and Standard Deviation of a Probability Distribution µ =  [ x P(x) ] Mean  2 =  [ (x – µ) 2 P(x )] Variance  2 =  [ x 2 P(x )] – µ 2 Variance (shortcut)  =  [ x 2 P(x )] – µ 2 Standard Deviation

6 Using TI-83/84 calculator Press the STAT button and choose EDIT Enter the x-values into the list L 1 and the P(x) values into the list L 2 Press the STAT button and choose CALC Choose 1-Var Stats and press ENTER Type in L 1 then, (comma) then L 2 on that line, you will see 1-Var Stats L 1,L 2 Press ENTER You will see x-bar=…, it is actually  (mean) and  x=…, it is actually  (st. deviation)

7 Methods for Finding Normal Distribution Areas

8 Normal Distribution by TI-83/84 Press 2 nd VARS to get the DISTR menu Scroll down to normalcdf( and press ENTER Type in two values: Lower, Upper (separated by commas) and close the parenthesis You see a line like normalcdf(-2.00,1.50) Press ENTER and read the probability.

9 Normal Distribution by TI-83/84 (continued) If you do not have an upper value, type 999. Example: for P(z>1.2) enter normalcdf(1.2,999) If you do not have a lower value, type Example: for P(z<0.6) enter normalcdf(-999,0.6)

10 Inverse Normal by TI-83/84 Press 2 nd VARS to get the DISTR menu Scroll down to invNorm( and press ENTER Type in the desired area and close the parenthesis You see a line like invNorm(0.95) Press ENTER and read the z-score. Round off to three decimal places.

11 Normal Distribution by TI-83/84 Press 2 nd VARS to get the DISTR menu Scroll down to normalcdf( and press ENTER Type in four values: Lower, Upper, Mean, St.Deviation (separated by commas) and close the parenthesis You see a line like normalcdf(-999,174,172,29) Press ENTER and read the probability.

12 Inverse Normal by TI-83/84 Press 2 nd VARS to get the DISTR menu Scroll down to invNnorm( and press ENTER Type in the desired area, mean, st.deviation and close the parenthesis You see a line like invNorm(0.995,172,29) Press ENTER and read the x-score.