Question 1051715: Hello:
I can solve the following using the formula but cannot figure out how to do this problem using the binomial table.
Approximately 10% of American High School students drop out of school before graduation. Choose 10 students entering High School at random. Find the probability that at least 6 will graduate. Meaning P(graduating) = 100%-10% = 90% or p = .90 = 90% or p=.90 I changed it from 10.3% to 10% so p is 90% or .90, so that you can use the table to find the answer instead of the formula. Remember use 90% and use the table in the back of the text, Table B, not the formula for this one.
I understand that (6 <= x < 10)
The book gives X = .001 (is this the probability
How did they get .001 for X
How did they get q = 0.1
Did X = 5 come from the fact that x = 6, 7, 8, 9, 10
Help is greatly appreciated
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! your problem states that 10% of american high school students drop out before graduation.
this means that 90% will graduate.
when you take a sample of 10 students out of the population and you want to know the probability that 6 or more out of the 10 will graduate, then you are most likely looking at a binomial probability.
the binomial probability is used when you either have success or failure and nothing in between
success in this case is the probability that the student will graduate.
failure im this case is the probability that the student will not graduate.
since there are only two probabilities total, the probability of failure is always 1 minus the probability of success.
similarly, since there are only two probabilities total, the probability of success is always 1 minus the probability of failure.
since the probability of success is the probability that the students will graduate, then p = probability of success = .9.
since the probability of failure is the probability that the students will not graduate (drop out), then q = .1.
the binomial formula is:
p(x) = c(n,x) * p^x * q^(n-x).
c(n,x) is the combination formula of n! / (x! * (n-x)!).
the sum of all probabilities always has to be equal to 1.
i used excel to calculate all the probabilities of p(x) from x = 0 to x = 10.
the result are shown below:
you can see from this table, that the probability of getting AT LEAST 6 out of the 10 students, chosen at random from the general population, to be among the 10% of the general population that will drop out is 0.998365063, which is equal to .998 if you round to 3 decimal places.
what you do is you calculate for p(6), p(7), p(8), p(9), p(10).
you then add them up to get the probability of p(x) from x = 6 to 10.
that becomes the probability that at least 6 out of the 10 students will graduate.
here's a reference on binomial probability that might help you to understand.
http://www.regentsprep.org/regents/math/algtrig/ats7/blesson.htm
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