SOLUTION: There is a 100 question multiple choice test each with 5 choices. You randomly guess each question.
Set up the binomial probability formula to find the probability of getting e
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Question 933339: There is a 100 question multiple choice test each with 5 choices. You randomly guess each question.
Set up the binomial probability formula to find the probability of getting exactly 80 correct out of 100.
Check to see if you can use the normal approximation to binomial probabilities. then use normal approximation to compute the probability of getting 80 or more correct.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the formula for binomial probability is:
p(x) = c(n,x) * p^x * (1-p)^(n-x)
when n = 100 and x = 80, and p = 1/5 and q = 4/5, this formula becomes:
p(80) = c(100,80) * (1/5)^80 * (4/5)^20 which becomes:
p = 7.47051786 * 10^-38
that is a very small number which would be equal to 0 if you did any rounding to less than 35 decimal places.
the normal distribution approximation of this would be based on the following formula:
p = 1/5
q = 4/5
n = 100
s = sqrt(n*p*q) = 4
m = 100 * 1/5 = 20
the probability of getting exactly 80 is not possible, but can be approximated by finding the probability of getting between 79.5 and 80.5.
you would need to find the z-score of 79.5 and the z-score of 80.5
z-score = (x-m)/s
for 79.5, this becomes z = (79.5 - 20) / 4 which becomes 59.5 / 4 which becomes 14.875.
for 80.5, this becomes z = (80.5 - 20) / 4 which becomes 60.5 / 4 which becomes
15.125
the numbers are off the charts which makes the probability effectively 0 which agrees with the result of the binomial probability.
most normal distribution statistical tables, if not all, don't get down into the mud that far.
since the mean is 20, this means you have a 50% probability of getting more than 20% right.
the numbers get worse from there.
more than 20 right p = .5
more than 30 right p = .0062
more than 40 right p = 0
the calculator can't dig into the mud that far and shows 0.
note that this is not the probability of getting exactly 40 right.
this is the probability of getting 40 or more right.
the probability of getting exactly 40 right is even less, but both are so small as to not be able to be measured using the normal distribution curve table or calculators that are online.
fyi, c(100,80) is the combination formula of n! / (x! * (n-x)!)
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