In a TF exam with 100 questions passing requires a score of

In a T-F exam with 100 questions, passing requires a score of at least 60. What is the approximate normal probability that a \"guesser\" will score at least 60 points?

Solution

METHOD 1:

Binomial Distribution

PMF of B.D is = f ( k ) = ( n k ) p^k * ( 1- p) ^ n-k
Where   
k = number of successes in trials
n = is the number of independent trials
p = probability of success on each trial
P( X < 60) = Used the excel formula = ROUND(BINOMDIST(60-1,100,0.50,TRUE),3)
= 0.9716
P( X > = 60 ) = 1 - P( X < 60) = 0.0284

METHOD 2:

Normal Approximation to Binomial Distribution
Mean ( np ) =100 * 0.5 = 50
Standard Deviation ( npq )= 100*0.5*0.5 = 5
Normal Distribution = Z= X- u / sd                   
P(X < 60) = (60-50)/5
= 10/5= 2
= P ( Z <2) From Standard NOrmal Table
= 0.9772                  

P(X >= 60) = 1- P(X < 60)
= 0.0228