Question 1171779
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            It is a binomial distribution type problem.


            I will use the Excel standard function BINOM.DIST to facilitate calculations.

            It has the analogue --- the standard function binompdf in pocket calculators TI-83 and TI-84.



<pre>
Probability that at most three of 8 do believe is 


    P = P(0) + P(1) + P(2) + P(3) = {{{sum(C(8,k)*0.25^k*(1-0.25)^(8-k),k=0,3)}}} = BINOM.DIST(3, 8, 0.25, TRUE) = 0.8862 = 88.62%.      <U>ANSWER</U>


The Excel standard function BINOM.DIST allows calculating this sum in one click.
</pre>

Solved.


On Excel function BINOM.DIST, see its description everywhere, for example

https://support.office.com/en-us/article/binom-dist-function-c5ae37b6-f39c-4be2-94c2-509a1480770c



On binompdf function for pocket calculators TI-83 and TI-84 see the link

http://users.rowan.edu/~schultzl/ti/binomial.pdf



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If you want to see other similar solved problems, 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>Solving problems on Binomial distribution</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 using Technology</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</A> 

in this site.