What is the probability of getting 80% on a True/ False 14 question test?

What is the probability of getting 80% on a True/ False 14 question test?





A) 1


B) .212


C) .395


D) .183What is the probability of getting 80% on a True/ False 14 question test?
80% of 14 is 11.2 so it is technically impossible to get 80% correct answers on a 14 question true falls exam.





in general we have the following.





Let X be the number of correct answers on the exam. X has the binomial distribution with n = 14 trials and success probability p = 0.5





In general, if X has the binomial distribution with n trials and a success probability of p then


P[X = x] = n!/(x!(n-x)!) * p^x * (1-p)^(n-x)


for values of x = 0, 1, 2, ..., n


P[X = x] = 0 for any other value of x.





The probability mass function is derived by looking at the number of combination of x objects chosen from n objects and then a total of x success and n - x failures.


Or, in other words, the binomial is the sum of n independent and identically distributed Bernoulli trials.





X ~ Binomial( n = 14 , p = 0.5 )





the mean of the binomial distribution is n * p = 7


the variance of the binomial distribution is n * p * (1 - p) = 3.5


the standard deviation is the square root of the variance = 鈭?( n * p * (1 - p)) = 1.870829





The Probability Mass Function, PMF,


f(X) = P(X = x) is:





P( X = 0 ) = 6.103516e-05


P( X = 1 ) = 0.0008544922


P( X = 2 ) = 0.005554199


P( X = 3 ) = 0.02221680


P( X = 4 ) = 0.06109619


P( X = 5 ) = 0.1221924


P( X = 6 ) = 0.1832886


P( X = 7 ) = 0.2094727


P( X = 8 ) = 0.1832886


P( X = 9 ) = 0.1221924


P( X = 10 ) = 0.06109619


P( X = 11 ) = 0.02221680


P( X = 12 ) = 0.005554199


P( X = 13 ) = 0.0008544922


P( X = 14 ) = 6.103516e-05What is the probability of getting 80% on a True/ False 14 question test?
impossible. you have 2 choices for each question, no partial credit.


getting an 11/14 is a 71% and 12/14 is 85%





you can't get an 80.