CK-12 Probability and Statistics - Advanced

4.4. The Binomial Probability Distribution http://www.ck12.org

Using the complementation rule,

p(x> 12 ) = 1 −[p( 1 )+p( 2 )+...+p( 12 )]

= 1 −p(x≤ 12 )

=

12

∑

x= 0

1 −p(x)

Consulting tables or calculators (see Box below, Technology Note),k= 12 ,p=.6, we get the result 0.584. Thus

P(x> 12 ) = 1 − 0. 584 = 0. 416

d. To find the probability of exactly 11 voters favor the candidate,

p(x= 11 ) =p(x≤ 11 )−p(x≤ 10 ) =. 404 −. 245 =. 159

Technology Note

The TI-83/84 calculators and the EXCEL spreadsheet have commands for the Binomial distribution.

• Press[DIST]and scroll down (or up) tobinompdf(Press[ENTER]to placebinompdfon your home screen.)
  Type values ofμandxseparated by commas and press[ENTER].


• Usebinomcdf( for probability ofatmostx) successes.

Note:it is not necessary to close the parentheses.

UsingEXCEL

• In a cell, enter the function =binomdist(x,n,p,false). Press[Enter]and the probability ofxsuccesses will
  appear in the cell.


• For probability ofatleastxsuccesses, replace “false” with “true”

Lesson Summary

1. Characteristics of aBinomial Experiment
   
   
   • The experiment consists ofnnumber of identical trials.
   
   
   • There are only two possible outcomes on each trial:S(for Success) orF(for Failure).
   
   
   • The probability ofSremains constant from trial to trial. We will denote it byp. We will denote the probability
     ofFbyq. Thusq= 1 −p.
   
   
   • The trials are independent of each other.
   
   
   • The binomial random variablexis the number ofS′sin thentrials.