SOLUTION: It is estimated that 20% of luxury cars manufactured in 2019 were silver. A car dealership typically sells 20 luxury cars per month. The probability that more than 10 of the luxury

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Question 1150527: It is estimated that 20% of luxury cars manufactured in 2019 were silver. A car dealership typically sells 20 luxury cars per month. The probability that more than 10 of the luxury cars sold per month are silver is:
Answer by ikleyn(52832) 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%2820%2Ck%29%2Ap%5Ek%2Aq%5E%2820-k%29%2Ck=11%2C20%29      (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%28C%2820%2Ck%29%2Ap%5Ek%2Aq%5E%2820-k%29%2Ck=0%2C10%29.     (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%28C%2820%2Ck%29%2A0.2%5Ek%2A%281-0.2%29%5E%2820-k%29%2Ck=0%2C10%29 = 0.999437.    


In this way, the value of  (2)  is equal to  1 - 0.999437 = 0.000563 (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