# Approximation to Binomial Distribution

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If np â‰¥ 5 and nq â‰¥ 5 estimate P (fewer than 2) with n= 13 and p= 0.4 by using the normal distribution as an approximation to the binomial distribution if np < 5 or nq <5 then state that the normal approximation is not suitable.

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P ( fewer than 2)=

The normal approximation is not suitable

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## SOLUTION This solution is **FREE** courtesy of BrainMass!

Now, np=13*0.4=5.2>5, and nq=13*(1-0.4)=7.8>5, so normal approximation is suitable

So mean= np=13*0.4=5.2 and sd=sqrt(13*0.4*0.6)=1.766

Since z=(x-mean)/sd

P( fewer than 2)=P(Z<(2-5.2)/1.766)=P(Z<-1.81)=0.0352 from standard normal table

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