Question

If x is a binomial random variable where n = 100 and p = 0.20, find the probability that x is more than 18 using the normal approximation to the binomial. Check the condition for continuity correction.

Answer 1

Given : n = 100 p = 0.20 therefore , q = 1 - p = 0.80

Also ,

Since , np = 100*0.20 = 20 > 10 and nq = 100*0.80 = 80 > 10

Therefore , by using the normal approximation to the binomial distribution ,

We want to find the P(X > 18)

Therefore , = n * p =  100*0.20 = 20

= n * p * q = 100 * 0.20 * 0.80 = 4

Therefore ,

P(X > 18) = 1 - P(X > 18) = 1 - P((x - ) / < (18- 20) / 4) = 1 - P(Z < -0.5) = 1-0.3085 = 0.6915