Question 1083819
this is an application of the binomial probability distribution
:
in a true/false test, you have a 50% chance of guessing correctly
:
a) Probability(P) (8 correct choices out of 10 trials) = 10C8 * (0.50)^8 * (1-0.50)^(10-8) = 0.04
:
Note 10C8 = 10! / (8! * (10-8)!)
:
b)  mean = 10 * 0.50 = 5, standard deviation = square root(10 * 0.50 * (1-0.50)) = 1.58
:
c)  yes, from b the student can not achieve passing grade by guessing.  If the test has 5 true and 5 false correct answers, best the student can do is 5.  If there is an unequal amount of true and false correct answers, the spread is (3.42 to 6.58)
: