SOLUTION: find the indicated probabilities. about 30% of U.S. adults are trying to lose weight. you randomly select eight U.S. adults. find the probability that the number of U.S. adults who

Algebra ->  Statistics  -> Binomial-probability -> SOLUTION: find the indicated probabilities. about 30% of U.S. adults are trying to lose weight. you randomly select eight U.S. adults. find the probability that the number of U.S. adults who      Log On


   

Question 1195775: find the indicated probabilities. about 30% of U.S. adults are trying to lose weight. you randomly select eight U.S. adults. find the probability that the number of U.S. adults who say they are trying to lose weight is (a) exactly three, (b) at least three, and (c) more than three
Found 2 solutions by Boreal, ikleyn:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
This is binomial because n is fixed, assume constant probability and independence of random samples.
a. 8C3*0.3^3*0.7^5=0.2541
b. look at 0,1,2
for 0 it is 0.7^8=0.0576
for 1 it I 8*0.3*0.7^7=0.1977
for 2 it is 28*0.3^2*0.7^6=0.2965
The sum of those is 0.5088
so at least 3 is everything else or 1-0.5088 or 0.4912 .
c. More than 3 is 0.4912-0.2541, which is exactly 3=0.2371

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
find the indicated probabilities. about 30% of U.S. adults are trying to lose weight.
you randomly select eight U.S. adults. find the probability that the number of U.S. adults
who say they are trying to lose weight is
(a) exactly three,
(b) at least three, and
(c) more than three
~~~~~~~~~~~~~~~~~~~~


            Tutor @Boreal misread the problem and gave incorrect answers.

            So I came to bring a correct solution.


It is a typical binomial distribution probability problem. 

(a)  Use the standard formula

         P(exactly 3 of 8) = C%5B8%5D%5E3%2A0.3%5E3%2A%281-0.3%29%5E%288-3%29 = 56%2A0.3%5E3%2A0.7%5E5 = 0.2541  (rounded).    ANSWER


(b)  The standard formula is

         P(at least 3 of 8) = P(3) + P(4) + P(5) + P(6) + P(7) + P(8) = 

                            = P(n=8; k>=3; p=0.3) = sum%28C%5B8%5D%5Ek%2A0.3%5Ek%2A%281-0.3%29%5E%288-k%29%2C+k=3%2C8%29.


         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 = 0.44822  (rounded).    ANSWER



(c)  P(more then 3 of 8) = P(at least 3 of 8) - P(exactly 3 0f 8) = the number from (b)  highlight%28MINUS%29  the number from (a) = 

                         = 0.44822 - 0.2541 = 0.19412 (rounded).    ANSWER

Solved :   all questions are answered  (correctly).

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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).