Question 1150527
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<pre>

This is a binomial distribution type problem where the probability under the question is the sum


     P = {{{sum (C(20,k)*p^k*q^(20-k),k=11,20)}}}      (1)


The number of trials is              20;
The indexes of success trials        k = 11,12,13,14,15,16,17,18,19,20
The probability of success trial     p = 0.2;
                                     q = 1 - p
C(n,k) = n! / (k! * (n-k)!)          are binomial coefficients.


The sum  (1)  is equal to  1 - {{{sum(C(20,k)*p^k*q^(20-k),k=0,10)}}}.     (2)



Instead of calculating every term of (2) manually and then summing them up, you may use Excel function 

BINOM.DIST(10, 20, 0.2, TRUE)  to calculate the cumulative sum value


    {{{sum(C(20,k)*0.2^k*(1-0.2)^(20-k),k=0,10)}}} = 0.999437.    


In this way, the value of  (2)  is equal to  1 - 0.999437 = 0.000563 (approximately).    <U>ANSWER</U>
</pre>

Thus the problem is solved using Technology.


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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