SOLUTION: ​69% of U.S. adults have very little confidence in newspapers. You randomly select 10 U.S. adults. Find the probability that the number of U.S. adults who have very little confid

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Question 1176192: ​69% of U.S. adults have very little confidence in newspapers. You randomly select 10 U.S. adults. Find the probability that the number of U.S. adults who have very little confidence in newspapers is ​ (a) exactly​ five, (b) at least​ six, and​ (c) less than four.
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.
69% of U.S. adults have very little confidence in newspapers. You randomly select 10 U.S. adults.
Find the probability that the number of U.S. adults who have very little confidence in newspapers is ​
(a) exactly​ five, (b) at least​ six, and​ (c) less than four.

Solution 

(a)  It is a binomial distribution probability problem.

     - number of trials        n =  10;
     - number of success trial k =   5;
     - Probability of success on a single trial p = 0.69.



We need calculate  P(n=10; k = 5; p=0.69).      


To facilitate calculations, I use an online (free of charge) calculator at this web-site 

https://stattrek.com/online-calculator/binomial.aspx


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


    P(n=10; k = 5; p=0.69) = 0.11283776194,   or   0.1128 (rounded).       ANSWER




(b)  It is a binomial distribution probability problem.

     - number of trials        n =  10;
     - number of success trial k >=  6;
     - Probability of success on a single trial p = 0.69.



We need calculate  P(n=10; k >=  6; p=0.69).      


Use online (free of charge) calculator at this web-site 

https://stattrek.com/online-calculator/binomial.aspx


    P(n=10; k >= 6; p=0.69) = 0.83205254038,   or   0.8321 (rounded).       ANSWER



(c)  It is a binomial distribution probability problem.

     - number of trials        n =  10;
     - number of success trial k <   4;
     - Probability of success on a single trial p = 0.69.



We need calculate  P(n=10; k < 4; p=0.69).      


Use online (free of charge) calculator at this web-site 

https://stattrek.com/online-calculator/binomial.aspx


    P(n=10; k < 4; p=0.69) = 0.0128636757,   or   0.0129 (rounded).       ANSWER


Solved.

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

To see a variety similar 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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