If np >5 and nq>5 estimate P (fewer than 4) with n=13 p=0.4 by using normal distribution as an approximate to the binomial

Question

liq [111]

3 years ago

13

If np >5 and nq>5 estimate P (fewer than 4) with n=13 p=0.4 by using normal distribution as an approximate to the binomial

distribution if np <5 or nq< then state that the normal approximation is not suitable.

Mathematics

1 answer:

9966 [12] · Answer 1 · 2022-06-15T17:51:42+03:00

The Normal approximation to the binomial

is as follows

mean=13(.5)=6.5 
variance=6.5(.5)=3.25 
Pr[fewer than 4]= 
Pr[N<=3] Apply the continuity correction 
Pr[N<=3.5]~=Pr[Z<3.5-6.5/sqrt(3.25)]=

Pr[Z<-1.66]=0.048457226

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