The probability that a washing machine is in need of repair

The probability that a washing machine is in need of repair is 50%. If an apartment complex has 100 washing machines, what is the probability that at least 60 will be in need of repair? Use the normal approximation to the binomial, applying the appropriate Continuity Correction Factor.

Solution

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