It is claimed that 95% of people in a certain village are right handed. A random sample of 80 villagers are tested to see if they are right or left handed. Use a Poisson approximation to estimate that the number of people that are right handed is:
a) 80 b) 79 c) at least 78
So I know at first this is a binomial question...n=80p=0.95
Im going to use z instead of lambda because I Dont know how to make a lambda on the computer :P So XPo(z)
z = mean = np
so np = z
z = 0.95 x 80 = 76
XPo(76)
P(X=x)=e−z×x!zx
So P(X=80)=e−76×80!7680 And I got a math error (because the numbers are too small for the calculator i presume)
I know its probably easier to use a binomial distribution as n is large but p is not small...but the question says use poisson =/
Where have I gone wrong? Or is the book stupid? :P