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 (
,
)**

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