Determine whether each of the following binomial distributions can be approximated using a normal distribution.

Question

Determine whether each of the following binomial distributions can be approximated using a normal distribution.

A) 𝑛=50 B) 𝑛=40

𝑝 = 0.4 𝑝 = 0.12

Answer 1

Hello Rav,

For a fixed value of p, as the value of n increases the shape of the binomial distribution for a random variable becomes bell shaped (or approximately normal). As a rule of thumb, we check the normality condition

np(1-p)>=10 to determine whether a normal distribution may be used to approximate a binomial distribution.

Part a) we are given n = 50 and p = 0.4

Substituting into the normality condition we have,

50*(0.4)*(1-0.4) = 12 >=10

So, we conclude that, yes a normal probability distribution may be used.

Part b) we are given n = 40 and p = 0.12

Substituting into the normality condition we have,

40*(0.12)*(0.88) = 4.224 < 10

Hence, no a normal probability may not be used.