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Difference between revisions of "Manuals/calci/BINOMDIST"
 
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<div style="font-size:30px">'''BINOMDIST (NS, TS, PS, CU)'''</div><br/>
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<div style="font-size:30px">'''BINOMDIST (numbers, trials, probability, cumulative)'''</div><br/>
 +
 
 +
*<math>numbers</math> is the number of successes in trials.
 +
*<math>trials</math> is the number of independent trials.
 +
*<math>probability</math> is the probability of success on each trial.
 +
*<math>cumulative</math> is a logical value that determines the form of the function.
 +
**BINOMDIST(), returns the individual term binomial distribution probability.
  
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*<math>NS</math>is the number of successes in trials.
 
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*<math>TS</math> is the number of independent trials.
 
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*<math>PS</math> is the probability of success on each trial
 
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*<math>CU</math> is a logical value that determines the form of the function.
 
 
==Description==
 
==Description==
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This function gives the individual element Binomial Distribution Probability.We can use this function when the following conditions are satisfied:
+
 
 +
*This function gives the individual element Binomial Distribution Probability.  
 +
*We can use this function when the following conditions are satisfied:
 
#A number of tests <math>n</math> should be fixed.
 
#A number of tests <math>n</math> should be fixed.
 
#Each test must be independent.
 
#Each test must be independent.
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#No test has  any impact on any other test.  
 
#No test has  any impact on any other test.  
 
  For example, the number of ways to achieve 2 heads in a set of four tosses is "4 choose 2".
 
  For example, the number of ways to achieve 2 heads in a set of four tosses is "4 choose 2".
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*In BINOMDIST function, NS is the number of successes  in trials.
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*In BINOMDIST function, <math>numbers</math> is the number of successes  in trials.
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*TS is the number trials to be made, also NS and TS should be integers.
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*<math>trials</math> is the number trials to be made, also <math>numbers</math> and <math>trials</math> should be integers.
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*And PS is number of probability of success on each independent trials.  
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*<math>probability</math> is the number of probability of success on each independent trials.  
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*Finally CU is the logical value like TRUE or FALSE. If it is TRUE  it will give the cumulative value or FALSE it will give the exact probability.
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*<math>cumulative</math> is the logical value like TRUE or FALSE. If it is TRUE  it will give the cumulative value or FALSE it will give the exact probability.
 
This function gives result as "Error" when  
 
This function gives result as "Error" when  
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#NS and TS are not an Integer.  
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#<math>numbers</math> and <math>trials</math> are not an Integer.  
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#NS,TS and PS are not a numeric.
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#<math>numbers,trials,probability</math> are not a numeric.
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#NS < 0 or NS > TS.
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#<math>numbers < 0</math> or <math>numbers > trials</math>
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#Also PS < 0 or PS > 1.
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#Also <math>probability < 0</math> or <math>probability >1</math>
 +
For Example: =BINOMDIST (4, 12, 0.3, FALSE) is 0.2311
 +
 
 +
*The binomial distribution with parameters n and p, we write <math> X \tilde{} B(n, p)</math>.
 +
*The probability of getting exactly <math> k </math> successes in <math> n </math> trials is given by the Probability Mass Function:
 +
<math> b(k;n,p)=Pr(X = k) = \binom{n}{k}p^{k}(1-p)^{n-k}</math> for k=0,1,2,3...n where  <math>\binom{n}{k}</math> is the COMBIN(n,k) i.e.<math> \binom{n}{k} = \frac{n!}{k!(n-k)}!</math>
  
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The binomial distribution with parameters n and p, we write <math> X \tilde{} B(n, p)</math>.
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*The Cumulative Binomial Distribution is:<math>B(x;n,p) = Pr(X \le x) =\sum_{i=0}^x  \binom{n}{i}p^{i}(1-p)^{(n-i)}</math>
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The probability of getting exactly <math> k </math> successes in <math> n </math> trials is given by the Probability Mass Function:
 
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<math> b(k;n,p)=Pr(X = k) = \binom{n}{k}p^{k}(1-p)^{n-k}</math> for k=0,1,2,3...n where (n,k)is the COMBIN(n,k) i.e.<math>(n,k)=\frac{n!}{k!(n-k)}!</math>
 
  
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The Cumulative Binomial Distrbution is:<math>B(x;n,p) = Pr(X \le x) =\sum_{n=0}^x  \binom{n}{i}p^{i}(1-p)^{(n-i)}</math>
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==ZOS==
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*It calculates the individual term Binomial Distribution Probability.
 
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*ns and ts are integers.
 
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*When ns or ts or ps is non-numeric BINOMDIST displays error.
 
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*When ns is less than 0 or greater than t, BINOMDIST shows NaN.
 
  
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When ps is less than 0 or greater than 1, BINOMDIST calculates the wrong result.
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*The syntax is to calculate <math>BINOMDIST(numbers,trials,probability,cumulative)</math>
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= BINOMDIST (4, 12, 0.3, FALSE) is 0.2311
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*<math>numbers</math> is the number of successes in trials.
 +
*<math>trials</math> is the number of independent trials.
 +
*<math>probability</math> is the probability of success on each trial.
 +
*<math>cumulative</math> is indicating the form of the function.
 +
*For e.g.BINOMDIST(9,12,0.2,false)
 +
{{#ev:youtube|v=3PWKQiLK41M|280|center|Binomial Distribution}}
  
 
==Example==
 
==Example==
 +
 
#Toss a coin for 12 times. What is the probability of getting exactly 7 heads.
 
#Toss a coin for 12 times. What is the probability of getting exactly 7 heads.
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#*Here NS=7,TS=12,and PS=1/2=0.5
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#*Here ns=7,ts=12,and ps=1/2=0.5
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#*BINOMDIST(7,12,0.5,FALSE)=0.193359375
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#The LMB Company manufactures tires.  They claim that only .007 of LMB tires are defective.  What is the probability of finding 2 defective tires in a random sample of 50 LMB tires?
 
#The LMB Company manufactures tires.  They claim that only .007 of LMB tires are defective.  What is the probability of finding 2 defective tires in a random sample of 50 LMB tires?
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#*Here NS=2,TS=50 and PS=0.007
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#*Here ns=2,ts=50 and ps=0.007
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#*BINOMDIST(2,50,0.007,false)=0.0428446
 
  
 
{| id="TABLE3" class="SpreadSheet blue"
 
{| id="TABLE3" class="SpreadSheet blue"
 
|- class="even"
 
|- class="even"
 
| Questions
 
| Questions
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! NS
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! ns
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! TS
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! ts
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! PS
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! ps
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! CU
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! cu
 
! Result
 
! Result
 
|-
 
|-
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|12
 
|12
 
|0.5(1/2)
 
|0.5(1/2)
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|False
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|FALSE
 
|0.193359375
 
|0.193359375
 
|- class="even"
 
|- class="even"
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|15
 
|15
 
|0.007
 
|0.007
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|False
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|FALSE
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|0.0428446
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|0.00469597319803066
 
|- class="odd"
 
|- class="odd"
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|Question3
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|2
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|10
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|0.2
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|TRUE
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|0.6777995264000007
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|- class="even"
  
 
|}
 
|}
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 +
==Related Videos==
 +
 +
{{#ev:youtube|WWv0RUxDfbs|280|center|Binomial Distribution}}
  
 
==See Also==
 
==See Also==
 +
 
*[[Manuals/calci/COMBIN | COMBIN]]
 
*[[Manuals/calci/COMBIN | COMBIN]]
 
*[[Manuals/calci/FACT | FACT]]
 
*[[Manuals/calci/FACT | FACT]]
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==References==
 
==References==
 
[http://en.wikipedia.org/wiki/Binomial_distribution  Binomial Distribution]
 
[http://en.wikipedia.org/wiki/Binomial_distribution  Binomial Distribution]
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 +
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*[[Z_API_Functions | List of Main Z Functions]]
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*[[ Z3 |  Z3 home ]]

Latest revision as of 02:30, 25 August 2020

BINOMDIST (numbers, trials, probability, cumulative)


  • Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle numbers} is the number of successes in trials.
  • Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle trials}  is the number of independent trials.
  • Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle probability}  is the probability of success on each trial.
  • Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle cumulative} is a logical value that determines the form of the function.
    • BINOMDIST(), returns the individual term binomial distribution probability.

Description

  • This function gives the individual element Binomial Distribution Probability.
  • We can use this function when the following conditions are satisfied:
  1. A number of tests Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle n} should be fixed.
  2. Each test must be independent.
  3. Each test represents only two results(Success/Failure)
  4. No test has any impact on any other test.
For example, the number of ways to achieve 2 heads in a set of four tosses is "4 choose 2".
  • In BINOMDIST function, Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle numbers} is the number of successes in trials.
  • Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle trials} is the number trials to be made, also Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle numbers} and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle trials} should be integers.
  • Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle probability} is the number of probability of success on each independent trials.
  • Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle cumulative} is the logical value like TRUE or FALSE. If it is TRUE it will give the cumulative value or FALSE it will give the exact probability.

This function gives result as "Error" when

  1. Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle numbers} and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle trials} are not an Integer.
  2.   are not a numeric.
  3. Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle numbers < 0} or Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle numbers > trials}
  4. Also Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle probability < 0} or Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle probability >1} 
For Example: =BINOMDIST (4, 12, 0.3, FALSE) is 0.2311
  • The binomial distribution with parameters n and p, we write Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle X \tilde{} B(n, p)} .
  • The probability of getting exactly Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle k } successes in Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle n } trials is given by the Probability Mass Function:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle b(k;n,p)=Pr(X = k) = \binom{n}{k}p^{k}(1-p)^{n-k}} for k=0,1,2,3...n where   is the COMBIN(n,k) i.e.Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \binom{n}{k} = \frac{n!}{k!(n-k)}!}

  • The Cumulative Binomial Distribution is:Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle B(x;n,p) = Pr(X \le x) =\sum_{i=0}^x \binom{n}{i}p^{i}(1-p)^{(n-i)}}

ZOS

  • The syntax is to calculate Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle BINOMDIST(numbers,trials,probability,cumulative)}
  • Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle numbers} is the number of successes in trials.
  • Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle trials} is the number of independent trials.
  • Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle probability} is the probability of success on each trial.
  • Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle cumulative} is indicating the form of the function.
  • For e.g.BINOMDIST(9,12,0.2,false)
Binomial Distribution

Example

  1. Toss a coin for 12 times. What is the probability of getting exactly 7 heads.
    • Here ns=7,ts=12,and ps=1/2=0.5
  1. The LMB Company manufactures tires. They claim that only .007 of LMB tires are defective. What is the probability of finding 2 defective tires in a random sample of 50 LMB tires?
    • Here ns=2,ts=50 and ps=0.007
Questions ns ts ps cu Result
Question 1 7 12 0.5(1/2) FALSE 0.193359375
Question2 2 15 0.007 FALSE 0.00469597319803066
Question3 2 10 0.2 TRUE 0.6777995264000007

Related Videos

Binomial Distribution

See Also

References

Binomial Distribution


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