Question

A binary experiment is repeated 900 times. What is the probability that there will be at least 495 successes if the success probability is 0.5?

Answer 1

Let X denote the number of successes. Then X\sim Bin(n=900,p=0.5)

Using Normal approximation to Binomial distribution,

$X\sim N(\mu=n \times p=450,\sigma^{2}=n \times p(1-p)=225)$

Required probability $= P(X\geq 495)=P(X>495.5)$

(Due to continuity correction as a result of using Normal approximation for Binomial distribution)

$=P(Z>\frac{495.5-450}{\sqrt{225}}) \\ =P(Z>3.03) \\ =1-P(Z<3.03) \\ =1-0.9987 \\ =0.0013$