SOLUTION: Suppose that 30% of all voters prefer Candidate A. If 6 people are chosen at random for a poll, what is the probability that fewer than 5 of them favor Candidate A? Probabili

Algebra ->  Probability-and-statistics -> SOLUTION: Suppose that 30% of all voters prefer Candidate A. If 6 people are chosen at random for a poll, what is the probability that fewer than 5 of them favor Candidate A? Probabili      Log On


   

Question 1185310: Suppose that 30% of all voters prefer Candidate A.
If 6 people are chosen at random for a poll, what is the probability that fewer than 5 of them favor Candidate A?
Probability =
(Please show your answer to 4 decimal places)
Found 2 solutions by ikleyn, Edwin McCravy:
Answer by ikleyn(52829) About Me  (Show Source):
You can put this solution on YOUR website!
.
Suppose that 30% of all voters prefer Candidate A.
If 6 people are chosen at random for a poll, what is the probability that fewer than 5 of them favor Candidate A?
Probability =
(Please show your answer to 4 decimal places)
~~~~~~~~~~~~~~~~~ 

It is a binomial distribution probability problem.

    - number of trials         n =  6;
    - number of success trials k <= 4;
    - Probability of success on a single trial p = 0.30.



We need calculate  P(n=6; k<=4; p=0.3).      


To facilitate calculations, I use an appropriate 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=6; k<=4; p=0.3) = 0.989065,   or   0.9891 (rounded).       ANSWER

Solved.

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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).



Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
Most students in most schools in America are required to have a TI-84 graphing
calculator.

You must interpret "fewer than 5" as "4 or fewer". 

Press: on clear

Press: 2nd vars

Use the down arrow to scroll to B:binomcdf(

Press: enter

Make the next screen read

        binomcdf
trials:6
p:0.30
x value:4
Paste

Use the down arrow key to scroll to highlight: Paste

Press: enter

You will see on the screen

binomcdf(6,0.30,4)

Press: enter

Read the answer 0.989065, round to 0.9891.

Edwin