Question 1052231: 53% of all persons in the U.S. population have at least some college education. Choose 10 persons at random. Find the probability that at least 5 do not have any college education.
Thanks!
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the probability that a person, chosen at random, has some college education is .53.
this means the probability that a person, chosen at random, does not have some college education is .47.
out of 10 people, you want to know the probability that at least 5 do not have a college education.
you would use the binomial probability formula, which is:
p(x) = c(n,x) * p^x * q^(n-x)
set p equal the probability that the person does not have any college education.
that makes p = .47
set q equal the probability that the person does have some college education.
that makes q = 1 - .47 = .53.
p(x) will now give you the probability that x persons do not have any college education.
if you want to know if at least 5 do not have any college education, then you want to find the sum of p(x) for x = 5 to x = 10.
the probability that at least 5 do not have any college education is equal to 0.547373025.
the attached spreadsheet shows the calculations.
this is the sum of p(x) for x = 5 to 10.
as an example of one of the calculations, let's use p(x) for x = 8.
the formula is p(x) = c(n,x) * p^x * q^(n-x)
when n = 10 and x = 8, this formula becomes p(8) = c(10,8) * .47^8 * .53^2.
since c(10,8) is equal to 10! / (8! * 2!) which is equal to 45, then:
p(8) = c(10,8) * .47^8 * .53^2 becomes p(8) = 45 * .47^8 * .53^2 which becomes p(5) = 0.030098657
you would manually do the same calculations for p(5), p(6), p(7), p(8), p(9), p(10).
alternatively, you can use excel.
there are also online binomial probability calculators that can do the work for you.
you just have to make sure you input the correct variables for the calculator to work.
one such calculator can be found here.
http://stattrek.com/online-calculator/binomial.aspx
a picture of my inputs and outputs from this calculator are shown below:
you would look for x >= 5 in this calculator.
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