Question

If a student just guesses on a True/False questions, there is 50% to guess the answer correctly. Suppose a True/False question exam contains 50 questions.

d) Find the approximate probability that a person who is just guessing will fail the test (got lower than 60% correct answers).

e) Find the approximate probability that a person who is just guessing will get a 70% or better.

Answer 1

Using normal approximation,

P(< p ) = P(Z < ( - p) / sqrt [ ( p( 1 - p) / n ) )

a)

P( < 0.60) = P(Z < ( 0.60 - 0.50) / sqrt [ 0.50 * 0.50 / 50 ] )

= P(Z < 1.41)

= 0.9207

b)

P( >= 0.70) = P(Z > ( 0.7 - 0.5) / sqrt ( 0.5 * 0.5 / 50) )

= P( z > 2.83)

= 1 - P(Z < 2.83)

= 1 - 0.9977

= 0.0023