Among all the income-tax forms filed in a certain year, the mean tax paid was $2

Question

Among all the income-tax forms filed in a certain year, the mean tax paid was $2,000 and the standard deviation was $500. In addition, for 10% of the forms, the tax paid was greater than $3, 500. A random sample of 625 tax forms is drawn. a. What is the probability that the average tax paid on the sample forms is greater than $1, 986? P(X bar > 1, 986) = 0.7580 b. What is the probability that more than 60 of the sampled forms have a tax of greater than $3, 500? Round the z-score to two decimal places. P(Y > 60) =

Explanation / Answer

a)here for 625 froms std error =std deviation/(n)1/2 =20

P(X>1986)=1-P(X<1986)=1-P(Z<(1986-2000)/20)=1-P(Z<-0.7)=1-0.2420=0.7580

b)as p=10%

mean =np=625*0.1=62.5

std deviation =(np(1-p))1/2=7.5

hence P(Y>60)=1-P(Y<=60)=1-P(Z<(60.5-62.5)/7.5)=1-P(Z<-0.2667)=1-0.3949=0.6051

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