Question

If x is a binomial random variable where n = 100 and p = 0.30, find the probability that x is more than 25 using the normal approximation to the binomial. Check the condition for continuity correction.

Answer 1

Variable X follows Binomial distribution as below

X~Bin(100,0.3)

Mean =Probability*sample size=0.3*100=30

Variance=Probability*(1-Probability)*Sample Size=0.3*0.7*100=21

Hence Normal approximation would be as below

X~N(30,21)

Now we need to check probability that Pr(X>25)=1-Pr(X<=25)
=1-Pr((X-30/21)<=(25-30/21))
=1-(z<=-6/21)
=1-(z<=-0.281)
=1-(0.3897)
=0.6103

Hence when Pr (X>25) is 0.6103 using normal approximation