Question

A binomial distribution has 100 trials (n = 100) with a probability of success of 0.25 (π = 0.25). to apply the normal distribution to approximate the binomial, what are the mean and standard deviation?

Answer 1

The expected value or mean of binomial distribution is given by,
E(X) = np = 100×0.25 = 25

probability of failure = 1-0.25=0.75
Variance[V(X)] = npq = 100×0.25×0.75 = 18.75

Standard deviation = √V(X) = √18.75 = 4.33