Binomial Distribution
Definition of a Binomial Probability Distribution.
1) The procedure has a fixed number of trials.
2) Each trial has only two outcomes.
3) The trials are independent.
4) The probabilities remain constant for each trial.
Some Notation
If A is the event that the number of successes is “less than 4” or “fewer than 4”, then
A= xi  4 and the P(A) = P( xi  4 ) = 1 - P( xi  4 ) .
If A is the event that the number of successes is “greater than 4” or “more than 4”, then
A= xi  4 and the P(A) = P( xi  4 ) = 1 - P( xi  4 ) .
If A is the event that the number of successes is “at least 4” or “4 or more”, then A =
xi  4 and P(A) = P( xi  4 ) = 1- P( xi  4 )
If A is the event that the number of successes is “at most 4” or “4 or less”, then A =
xi  4 and the P(A) = P( xi  4 ) = 1 – P( xi  4 ).
A Binomial Distribution Problem
NASA buys 10 critical parts for the space shuttle from a company that claims that their
parts will break down in harsh conditions only 6% of the time. If the shuttle can still
maintain itself with any 7 of the 10 parts working, what is the probability that the shuttle
will be alright in harsh conditions? Does this seem like an acceptable risk or should
NASA look elsewhere to buy these parts.
Ans. 0.99797
Setup (1/2 pt ea.)
n= _________________________________
p= ____________
S = _________________________________
q = ___________
F= _________________________________
Xi= ________________________
P(S) = __________
P(F) = ______________

 = _____________