Manuals/calci/BINOMDIST

BINOMDIST (ns, ts, ps, cu)

• $ns$ is the number of successes in trials.
• $ts$ is the number of independent trials.
• $ps$ is the probability of success on each trial.
• $cu$ is a logical value that determines the form of the function.

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 $n$ 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, $ns$ is the number of successes in trials.
• $ts$ is the number trials to be made, also $ns$ and $ts$ should be integers.
• $ps$ is the number of probability of success on each independent trials.
• $cu$ 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.

This function gives result as "Error" when

1. $ns$ and $ts$ are not an Integer.
2. $ns,ts,ps$ are not a numeric.
3. $ns<0$ or $ns>ts$
4. Also $ps<0$ or $ps>1$

For Example: =BINOMDIST (4, 12, 0.3, FALSE) is 0.2311

• The binomial distribution with parameters n and p, we write $X{\tilde {}}B(n,p)$.
• The probability of getting exactly $k$ successes in $n$ trials is given by the Probability Mass Function:

$b(k;n,p)=Pr(X=k)={\binom {n}{k}}p^{k}(1-p)^{n-k}$ for k=0,1,2,3...n where \binom{n}{k} is the COMBIN(n,k) i.e.${\binom {n}{k}}={\frac {n!}{k!(n-k)}}!$

• The Cumulative Binomial Distribution is:$B(x;n,p)=Pr(X\leq x)=\sum _{i=0}^{x}{\binom {n}{i}}p^{i}(1-p)^{(n-i)}$

ZOS Section

• The syntax is to calculate $BINOMDIST(numbers,trials,probability,cumulative)$
• $numbers$ is the number of successes in trials.
• $trials$ is the number of independent trials.
• $probability$ is the probability of success on each trial.
• $cumulative$ is indicating the form of the function.
• For e.g.BINOMDIST(9,12,0.2,false)

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	0.0428446
Question3	2	10	0.2	True	0.6777995

See Also

• COMBIN
• FACT

References

Binomial Distribution