According to a Pew Research Center November 2016 report‡ on the digital economy,

Question

According to a Pew Research Center November 2016 report‡ on the digital economy, “8% of Americans earned money from an online ‘gig’ platform in the last year”. (a) [4 points] If a simple random sample of 20 Americans is taken, find the probability that at most 3 in the sample have earned money from an online ‘gig’ platform in the last year. (b) [6 points] If a simple random sample of 350 Americans is taken, find the probability that at most 10% of the sample have earned money from an online ‘gig’ platform in the last year. Use the normal approximation for sample proportion.

Explanation / Answer

Part-a

X follows Binomial with n=20 and p=0.08

So, P(X<=3)=0.9294 using excel function =BINOMDIST(3,20,0.08,TRUE)

Part-b

X follows normal with mean =np=350*0.08=28 and

standard deviation =sqrt(np(1-p))=sqrt(350*0.08*(1-0.08))=5.08

So, P(X<=10%*350)==P(X<=35)=P(X<35.5) using continuity correction

Hence P(X<=35)=0.9301 using excel function =NORMDIST(35.5,28,5.08,TRUE)

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