Question 1196861
.
Assume the random variable X has a binomial distribution with the given probability 
of obtaining a success. Find the following probability, given the number of trials 
and the probability of obtaining a success. Round your answer to four decimal places.
P(X≤3), n=6, p=0.6
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            It is a standard binomial distribution problem.



<pre>
The number of trials is n=6;  the indexes of successful trials are k=0, 1, 2, 3; 
the probability of success for each single individual trial is p = 0.6).


     The formula to calculate the probability is


     P = P(0) + P(1) + P(2) + P(3) = P(n=6; k<=3; p=0.6) = {{{sum(C[6]^k*0.6^k*(1-0.6)^(6-k),k=0,3)}}} = {{{sum(C[6]^k*0.6^k*0.4^(6-k), k=0,3)}}}.


     To facilitate my calculations, I used online calculator at this site  https://stattrek.com/online-calculator/binomial.aspx

     It provides nice instructions  and  a convenient input and output for all relevant options/cases.


          The resulting number is P = 0.4557   (rounded).    <U>ANSWER</U>
</pre>

Solved.


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If you want to see many similar &nbsp;(or different) &nbsp;solved problems, &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 these lessons, &nbsp;you will be able to solve such problems on your own, 

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