Use normal approximation to estimate the probability of pass

Use normal approximation to estimate the probability of passing a true/false test of 30 questions if the minimum passing grade is 80% and all responses are random guesses. Use Excel to obtain more accuracy.

Solution

Normal Distribution
Proportion ( P ) =0.5
Standard Deviation ( sd )= Sqrt (P*Q /n) = Sqrt(0.5*0.5/30)
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
P(X > 0.8) = (0.8-0.5)/0.0913
= 0.3/0.0913 = 3.2859
= P ( Z >3.286) From Standard Normal Table
= 0.0005