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.
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 ( , )
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