A Binomial Random Variable has a rate parameter of 025 and a

A Binomial Random Variable has a rate parameter of 0.25, and a size parameter of 1000. Using the normal approximation of a binomial what is the probability that the binomial will be less than 225? Remember to use the continuity correct.

Question 18 options:

0.5718174

0.9409671

0.1476903

0.0312834

0.6457836

0.2564869

Solution

Normal Distribution
Mean ( np ) =250
Standard Deviation ( npq )= 1000*0.25*0.75 = 13.69306394
Normal Distribution = Z= X- u / sd                   
P(X < 225) = (225-250)/13.6931
= -25/13.6931= -1.8257
= P ( Z <-1.8257) From Standard NOrmal Table
= 0.0312834