Probablity question

Question

Assuming that our random variable Y belongs to Binomial distribution and Y∼ Binomial (n = 36, p = 1/3). Find the probability that Y > 14

Answer 1

for binomial mean = np = 36 * 1/3 = 12

and standard deviation = sqrt(n*p*(1-p)) = 2.83

want to find P( Y > 14)

Use normal approximation to binomial distribution with continuity correction:

z = ((Y - 0.5) - mean)/SD = ((Y-0.5) - 12)/2.83, so

P(Y > 14) = P(z > (14.5 - 12)/2.83) = P(z > 0.88) = P(z < -0.88) = 0.1894