Question

If x is a binomial random variable where n = 100 and p = 0.30, find the probability that x is greater than or equal to 35 using the normal approximation to the binomial. (Discuss whether continuity correction is required or not)

Answer 1

Solution :

Given that,

Using binomial distribution,

= n * p = 100 *9 0.30 = 30

= n * p * q = 100 * 0.30 * 0.70 = 2.5826

Using continuity correction ,

P(x 34.5) = 1 - P(x 34.5)

= 1 - P((x - ) / < (34.5 - 30) / 2.5826)

= 1 - P(z < 1.74)

= 0.0409

continuity correction is required .