A survey conducted in 2011 asked employed adults from age 25 to 70 if they plan

Question

A survey conducted in 2011 asked employed adults from age 25 to 70 if they plan to keep a foot in the working world after retirement. The percent of the respondents answering is presented in the table to the right. A random sample of adults from this age group was asked the same question below. Using the normal approximation to the binomial distribution based on the sample size indicated below, what is the probability that more than 18 adults from this sample would plan to keep a in the working world after retirement? Respondent answer Absolutely Respondent sample size was 100

Explanation / Answer

as probability to keep a foot in the working world after retirement p=0.19

n=100

hence mean =np=100*0.19=19

and std deviation =(np(1-p))1/2 =3.923

there fore P(X>18)=1-P(X<=18)=1-P(Z<(18.5-19)/3.923)=1-P(Z<-0.1275)=0.4493

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