Binomial distribution and finding the probability. I want to know how to use the binomial distribution table, given that the mean of a binomial distribution is 5 and the standard deviation is 2. What is the actual probability of 5 successes?

joguejaseg 2022-09-20 Answered
Binomial distribution and finding the probability
I want to know how to use the binomial distribution table, given that the mean of a binomial distribution is 5 and the standard deviation is 2. What is the actual probability of 5 successes? The(mean) is found by number of trials *probability of success in any trial; while the S.D. is found by square root of (number of trials) * (probability of success) * (probability of success-1). How do i use the binomial distribution table to find the probability or even without it, but without the use of permutations and combinations.
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Answers (2)

geoforoiunpwd
Answered 2022-09-21 Author has 6 answers
Step 1
At the first step, you must calculate the value of p.
m e a n = μ = n p = 5 ( 1 ) s d = 2 n p ( 1 p ) = 2 ( 2 )
( 1 ) , ( 2 ) 4 5 = 1 p p = 0.2 ( 3 )
( 1 ) , ( 3 ) n = 25
Step 2
In the binomial distribution table, you must find a row with n = 25 , x = 5 and column with p = 0.2.
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Dymnembalmese2n
Answered 2022-09-22 Author has 2 answers
Step 1
If you don´t have a table with n = 25 and a calculator which is able to calculate binomial coefficients directly you can decompose the binomial coefficient.
In general the asked probability is P ( X = k ) = ( n k ) p k ( 1 p ) n k
The binomial coefficient can be written as
( n k ) = n ( n 1 ) ( n k + 1 ) 1 2 k
Step 2
For n = 25 and k = 5 the probability is
P ( X = 5 ) = 25 24 23 22 21 1 2 3 4 5 0.2 5 0.8 20
This term can be calculated by the most calculators which are allowed in statistic lectures.
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