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.
• And PS is number of probability of success on each independent trials.
• 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.

This function gives result as "Error" when

1. NS and TS are not an Integer.
2. NS,TS and PS are not a numeric.
3. NS < 0 or NS > TS.
4. Also PS < 0 or PS > 1.

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 (n,k)is the COMBIN(n,k) i.e.${\binom {n}{k}}={\frac {n!}{k!(n-k)}}!$

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

• It calculates the individual term Binomial Distribution Probability.
• ns and ts are integers.
• When ns or ts or ps is non-numeric BINOMDIST displays error.
• When ns is less than 0 or greater than t, BINOMDIST shows NaN.

When ps is less than 0 or greater than 1, BINOMDIST calculates the wrong result. = BINOMDIST (4, 12, 0.3, FALSE) is 0.2311

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
   • BINOMDIST(7,12,0.5,FALSE)=0.193359375
2. 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
   • BINOMDIST(2,50,0.007,false)=0.0428446

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

See Also

• COMBIN
• FACT

References

Binomial Distribution