SOLUTION: Assume that when adults with smartphones are randomly​ selected, 57​% use them in meetings or classes. If 7 adult smartphone users are randomly​ selected, find the probabilit

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Question 1152814: Assume that when adults with smartphones are randomly​ selected, 57​% use them in meetings or classes. If 7 adult smartphone users are randomly​ selected, find the probability that at least 2 of them use their smartphones in meetings or classes.
Answer by ikleyn(52900) 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%287%2Ck%29%2Ap%5Ek%2Aq%5E%287-k%29%2Ck=2%2C7%29      (1)


The number of trials is              7;
The indexes of success trials        k = 2,3,4,5,6,7
The probability of success trial     p = 0.57;
                                     q = 1 - p
C(n,k) = n! / (k! * (n-k)!)          are binomial coefficients.


I am going to use the Excel standard function BINOM.DIST.

It provides calculations similar sums, but only in the case, when such sums are presented in so called cumulative form
as the sums from 0 to some integer number.


Therefore, I convert the sum (1) into the cumulative form.


In cumulative form, the sum  (1)  is equal to  1 - sum%28C%287%2Ck%29%2Ap%5Ek%2Aq%5E%287-k%29%2Ck=0%2C1%29.     (2)


Now, when the sum is presented in cumulative form, you may use the Excel function 

BINOM.DIST(1, 7, 0.57, TRUE)  to calculate 


    sum%28C%287%2Ck%29%2A0.57%5Ek%2A%281-0.57%29%5E%287-k%29%2Ck=0%2C1%29 = 0.02794.    


In this way, the value of  (2)  is equal to  1 - 0.02794 = 0.97206 (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


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To see other probability problems, solved by similar method, look into the lessons
    - Solving problems on Binomial distribution
    - How to calculate Binomial probabilities using Technology
    - Solving problems on Binomial distribution with Technology
in this site.