SOLUTION: It is asserted that 90 percent of the cars approaching an individual toll both in New Jersey are equipped with an E-Z pass transponder. Find the probability that in a 6 car sample.

Question 1146910: It is asserted that 90 percent of the cars approaching an individual toll both in New Jersey are equipped with an E-Z pass transponder. Find the probability that in a 6 car sample.
At least 3 will have the transponder?
Answer by ikleyn(52866) (Show Source): You can put this solution on YOUR website!
.

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


     P =       (1)


The number of trials is              6;
The indexes of success trials        k = 3, 4, 5, 6.
The probability of success trial     p = 0.9;
                                     q = 1 - p = 0.1;
C(n,k) = n! / (k! * (n-k)!)          are binomial coefficients.


The formula (1) is just a (ready to use) formal mathematical solution, and you may complete calculations manually.


But in nova days the trend is to use TECHNOLOGY for such calculations.

To use the Technology, notice that the sum  (1)  is equal to  1 - .     (2)


Instead of calculating every term of (1) or (2) manually and then summing them up, you may use Excel function 

BINOM.DIST(2, 6, 0.9, TRUE)  to calculate the value of    in one click

     = 0.00127.    


Therefore, the value of  (2)  is equal to  1 - 0.00127 = 0.99873 (approximately).    ANSWER

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

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