Question

Assume that x is a binomial random variable with n and p as specified below. For which cases would it be appropriate to use normal distribution to approximate binomial distribution? a. n=50, p=0.01 b. n=200, p=0.8 c. n=10, p=0.4

Answer 1

Solution :

If ,

n * p , n * q > 5 then we use  normal distribution to approximate binomial distribution .

a)

n = 50

p = 0.01

q = 1 - 0.01 = 0.99

n * p = 50 * 0.01 = 0.5

Here n * p < 5

Here, we can not use normal distribution to approximate binomial distribution .

b)

n = 200

p = 0.8

q = 1 - p = 1 - 0.8 = 0.2

n * p = 200 * 0.8 = 160 and

n * q = 200 * 0.2 = 40

Here , n * p , n * q > 5 so we can use normal distribution to approximate binomial distribution .

c) n = 10

p = 0.4

q = 1 - p = 1 - 0.4 = 0.6

n * p = 10 * 0.4 = 4 < 5

Here, we can not use normal distribution to approximate binomial distribution .