In a large population, a sample of 40 will not appreciably affect the probability of the population, hence the binomial distribution is applicable, namely
P(x)=C(n,x)p^x*(1-p)^(n-x)
p=0.35, n=40
a) E(x)=np
b) P(0)=C(n,x)p^(x)*(1-p)^(n-x)
=C(40,0)(0.35^0)(0.65^40)
c)P(x>=3)
=1-(P(0)+P(1)+P(2)
Substitute x=0,1 and 2 and evaluate P(x>=3)
The number of immigrants living in a certain country with a large population makes up 35% of the population. In a random sample poll of 40 people what is:
a)the expected number of non-immigrants will be polled?
b)the probability that no immigrants will be polled?
c)the probability that at least 3 immigrants will be polled?
Thanks.
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1 answer