Question

For which of the following binormial distributions are the conditions for the normal approximation to the binomial distribution satisfied?

		a. = 40, p = 0.9
		b. = 400, p = 0.99
		c. = 20, p = 0.2
		d. = 20, p = 0.3

Answer 1

For normal approximation to binomial, np > 5 and nq >5

a) n = 40

p - 0.9

q = 1 - 0.9 = 0.1

nq = 40x0.1 = 4

Conditions for normal approximation are not satisfied.

b) n = 400,

p = 0.99

q = 1 - 0.99 = 0.01

nq = 400x0.01 = 4

Conditions for normal approximation are not satisfied.

c) n = 20

p = 0.2

q = 1 - 0.2 = 0.8

np = 20x0.2 = 4

Conditions for normal approximation are not satisfied.

d) n = 20

p = 0.3

q = 1 - 0.3 = 0.7

np = 20x0.3 = 6

nq = 20x0.7 = 14

Both np and nq > 5

So, Conditions for normal approximation are satisfied

Ans: d) n = 20, p = 0.3