1. BUSINESS MATHEMATICS
&
STATISTICS

2. Patterns of probability: Binomial, Poisson and Normal Distributions
LECTURE 38
Patterns of probability: Binomial, Poisson and Normal Distributions
Part 2

3. CUMULATIVE BINOMIAL PROBABILITIES
Probability of r or more successes in n trials with the probability of success in each trial
Look in column for n
Look in column for r
Look at column for value of p(0.05 to 0.5)
Example
n = 5; r = 4;p = 0.5
p( 4 or more successes in 5 trials)
= = %

4. Returns the individual term binomial distribution probability
BINOMDIST
Returns the individual term binomial distribution probability
Use BINOMDIST in problems with a fixed number of tests or trials, when the outcomes of any trial are only success or failure, when trials are independent, and when the probability of success is constant throughout the experiment.
For example, BINOMDIST can calculate the probability that two of the next three babies born are male.

5. BINOMDIST BINOMDIST(number_s,trials,probability_s,cumulative)
Number_s   is the number of successes in trials.
Trials   is the number of independent trials.
Probability_s   is the probability of success on each trial.
Cumulative   is a logical value that determines the form of the function. If cumulative is TRUE, then BINOMDIST returns the cumulative distribution function, which is the probability that there are at most number_s successes; if FALSE, it returns the probability mass function, which is the probability that there are number_s successes.

8. EXAMPLE USING TABLES p(2 or less dry days) + p(3 or more dry days) = 1
n = 7; r = 3; p = 0.4
p(3 or more dry days) =
p(2 or less dry days) = =
= Chance of 5 or more wet days next week

10. EXAMPLE 8 bit message is transmitted electronically
p(one bit transmitted erroneously) = 0.1
What is the chance that entire message is transmitted correctly)?
n = 8; r = 8, p = 0.1; p(exactly 0 errors)?
p(0 errors) + p( 1 or more errors) = 1
P(0 errors) = 1 – p( 1 or more errors)
TABLES
= 1 – =

12. EXAMPLE A surgery is successful for 75% patients
p(success in at leaset 7 cases in randomly selected 9 patients)?
n = 9; p(success) = 0.75; p(at lease 7 cases)?
p = 0.75 is outside the table
p(failure) = 1 –0.75 = 0.25
Success at least 7 = Failure 2 or less
P(failure 2 or less) = 1 – p(failure 3 or more)
= 1 – = = 60%

14. Like the binomial, trials are assumed to be independent.
NEGBINOMDIST
Returns the negative binomial distribution NEGBINOMDIST returns the probability that there will be number_f failures before the number_s-th success, when the constant probability of a success is probability_s
This function is similar to the binomial distribution, except that the number of successes is fixed, and the number of trials is variable
Like the binomial, trials are assumed to be independent.

15. NEGBINOMDIST
Example
You need to find 10 people with excellent reflexes, and you know the probability that a candidate has these qualifications is 0.3
NEGBINOMDIST calculates the probability that you will interview a certain number of unqualified candidates before finding all 10 qualified candidates.

16. NEGBINOMDIST Syntax NEGBINOMDIST(number_f,number_s,probability_s)
Number_f   is the number of failures.
Number_s   is the threshold number of successes.
Probability_s   is the probability of a success.

18. CRITBINOM
Returns the smallest value for which the cumulative binomial distribution is greater than or equal to a criterion value
Use this function for quality assurance applications For example, use CRITBINOM to determine the greatest number of defective parts that are allowed to come off an assembly line run without rejecting the entire lot.
Syntax
CRITBINOM(trials,probability_s,alpha)
Trials   is the number of Bernoulli trials.
Probability_s   is the probability of a success on each trial.
Alpha   is the criterion value.

19. BUSINESS MATHEMATICS
&
STATISTICS

20. BUSINESS MATHEMATICS
&
STATISTICS