SOLUTION: In a survey, 3 of 4 students said the courts show “too much concern” for criminals. Find the probability that at most 3 of 7 randomly selected students will agree with thi

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Question 1186781: In a survey, 3 of 4 students said the courts show
“too much concern” for criminals. Find the probability that at most 3 of 7 randomly
selected students will agree with this statement.


Answer by ikleyn(52915)   (Show Source): You can put this solution on YOUR website!
.
In a survey, 3 of 4 students said the courts show
“too much concern” for criminals. Find the probability that at most 3 of 7 randomly
selected students will agree with this statement.
~~~~~~~~~~~~~~~~~


            In an encrypted form,  it is a binomial distribution probability problem. 


The number of trials is 7;  the number of successful trials is k <= 3; the probability of success for each single individual trial is p =  = 0.75.


     Therefore, the formula to calculate the probability is


         P(n=7; k<=3, p= 0.75) = 


     To facilitate my calculations, I used online calculator at this site  https://stattrek.com/online-calculator/binomial.aspx

     It provides nice instructions  and  a convenient input and output for all relevant options/cases.


          The resulting number is P = 0.07055664063 = 0.0706 = 7.06%  (rounded).    ANSWER

Solved.

---------------

If you want to see many similar  (or different)  solved problems,  look into the lessons
    - Simple and simplest probability problems on Binomial distribution
    - Typical binomial distribution probability problems
    - How to calculate Binomial probabilities with Technology (using MS Excel)
    - Solving problems on Binomial distribution with Technology (using MS Excel)
    - Solving problems on Binomial distribution with Technology (using online solver)
in this site.

After reading these lessons,  you will be able to solve such problems on your own,
which is your  PRIMARY  MAJOR  GOAL  visiting this forum  (I believe).



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