SOLUTION: According to StatsSa, the unemployment rate in South Africa as of 2018 has risen to 28%. For randomly selected group consisting of eight South Africans, what is the probability tha

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Question 1152070: According to StatsSa, the unemployment rate in South Africa as of 2018 has risen to 28%. For randomly selected group consisting of eight South Africans, what is the probability that at least two are unemployed?
Answer by ikleyn(52777) About Me  (Show Source):
You can put this solution on YOUR website!
.

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


     P = sum+%28C%288%2Ck%29%2Ap%5Ek%2Aq%5E%288-k%29%2Ck=2%2C8%29      (1)


The number of trials is              8;
The indexes of success trials        k = 2,3,4,5,6,7,8
The probability of success trial     p = 0.28;
                                     q = 1 - p
C(n,k) = n! / (k! * (n-k)!)          are binomial coefficients.


The sum  (1)  is equal to  1 - sum%28C%288%2Ck%29%2Ap%5Ek%2Aq%5E%288-k%29%2Ck=0%2C1%29.     (2)



You may calculate each term in (2) individually and then sum them up.


Or, alternatively, you may use Excel function  BINOM.DIST(1, 8, 0.28, TRUE)  to calculate the cumulative sum value


    sum%28C%288%2Ck%29%2A0.28%5Ek%2A%281-0.28%29%5E%288-k%29%2Ck=0%2C1%29 = 0.296906.    


In this way, the value of  (2)  is equal to  1 - 0.296906 = 0.703094 (approximately).    ANSWER

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