According to a census, approximately 5% of the population earned between $75,000

Question

According to a census, approximately 5% of the population earned between $75,000 and $100,000 annually in 2008. A random sample of 25 people in the population was selected.

a. Use the binomial distribution to determine the probability that fewer than three individuals earned between $75,000 and $100,000 annually in 2008.

b. Use the Poisson approximation to the binomial distribution to determine the probability that fewer than three individuals earned between $75,000 and $100,000 annually in 2008.

a) The probability is

b) The probability is

Explanation / Answer

Here n=25 and p=0.05

a. We need to find P(x<3) for binomial distribution

P(x)=ncxp^x(1-p)^n-x

So Px<3)=0.8729

b. Now mean=np=1.25 and sd-=sqrt(npq)=1.09

P(x<3) for Poisson distribution

P(x)=e-np*(np)^x/x!

P(x<3)=0.8685

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