Question

For the following conditions, determine if it is appropriate to use the normal distribution
to approximate a binomial distribution with n = 42 and p = 0.3. Explain you answer.

Answer 1

Solution:

Given that,

P = 0.3

1 - P = 0.7

n = 42

Here, BIN ( n , P ) that is , BIN (42 , 0.3)

then,

n*p = 12.6 > 5

n(1- P) = 29.4 > 5

According to normal approximation binomial,

X Normal

Mean = = n*P = 12.6

Standard deviation = =n*p*(1-p) = 8.82

Then

N ( , )