Question

Let x be a random variable from a binomial distribution with n = 40 and p = 0.9. If a normal approximation is appropriate, give the distribution of x' that would be used in the approximation.

a) x' ~ N(40, 0.9²)

b) x' ~ N(36, 3.6²)

c) x' ~ N(36, 1.9²)

d) normal approximation is not appropriate

Answer 1

For normal approximation of the binomial distribution we need two conditions to be met,

np>5 and np(1-p) >5

Here, np= 40"0.9 = 36

And np(1-p) = 3.6

Since the second condition is not met, option d) is correct.