Question 1202021
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        It is a typical binomial distribution probability problem.



<pre>
The number of trials is 12.

The probability of a single success trial is 36% = 0.36.

The number of success trials is between 4 to 6 inclusive, i.e. 4, 5, 6.



Use the standard formula for the probability


    P = {{{sum(C[12]^k*0.36^k*(1-0.36)^(12-k),k=4,6)}}} = 

      = {{{C[12]^4*0.36^4*0.64^8}}} + {{{C[12]^5*0.36^5*0.64^7}}} + {{{C[12]^6*0.36^6*0.64^6}}} = 

      = {{{495*0.36^4*0.64^8}}} + {{{792*0.36^5*0.64^7}}} + {{{924*0.36^6*0.64^6}}} = 0.5829  (rounded).    <U>ANSWER</U>
</pre>

Solved.


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If you want to see many other similar &nbsp;(and different) &nbsp;solved problems of this type, &nbsp;look into the lessons


&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/Solving-problems-on-Binomial-distribution-manually.lesson>Simple and simplest probability problems on Binomial distribution</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/Typical-binomial-distribution-probability-problems.lesson>Typical binomial distribution probability problems</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/How-to-calculate-binomial-probabilities-using-Technology.lesson>How to calculate Binomial probabilities with Technology (using MS Excel)</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/Solving-problems-on-Binomial-distribution-using-Technology.lesson>Solving problems on Binomial distribution with Technology (using MS Excel)</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/Solving-problems-on-Binom-distr-with-Technology-%28using-online-solver%29.lesson>Solving problems on Binomial distribution with Technology (using online solver)</A> 

in this site.


After reading from these lessons, &nbsp;you will be able to solve such problems on your own, &nbsp;which is your 

PRIMARY &nbsp;MAJOR &nbsp;GOAL &nbsp;visiting this forum &nbsp;(I believe).