in a city with 1 million residents, the unemployment rate is 4%. A random sample

Question

in a city with 1 million residents, the unemployment rate is 4%. A random sample of 20 residents is taken from the population, and the number of unemployed residents is counted a) consider the survey as a binomial experiment and complete the following: (show your work) i. n= ii.p= iii. X is the number of___ b)what is the probability that exactly 3 of the residents in the sample are unemployed? c)what is the probability that at most 3 of the residents in the sample are unemployed? d) what is the probability that at least 3 of the residents in the sample are unemployed?

Explanation / Answer

i. n=20

ii. p=4/100=0.04 and x is number of unemployed residents.

iii. P(x=3) here we will use binomial distribution P(X=x)=ncx*px*(1-p)n-x

So P(x=3)=20c3*0.043*(1-0.04)20-3=0.0364

iv. P(x<=3)=P(x=1 or 2 or 3)=0.9926

v. P(x>=3)=0.0439 which is probability for x=3 to 20

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