SunshineCity,whichattractsprimarilyretiredpeople,has90,000residentswithameanage of 72yearsandastandarddeviationof12years.Theagedistributionisskewedtotheleft.A random sampleof100residentsofSunshineCityhas y = 70 and s = 11.

(a) Describethecenter andspreadofthe(i)populationdistribution,(ii)sampledatadistri-

bution. Whatshapedoesthesampledatadistributionprobablyhave?Why?

(b) Findthecenterandspreadofthesamplingdistributionof Y for n = 100. Whatshape does ithaveandwhatdoesitdescribe?

(c) Explainwhyitwouldnotbeunusualtosampleapersonofage60inSunshineCity,but it wouldbehighlyunusualforthesamplemeantobe60,forarandomsampleof100 residents.

(d) Describethe sampling distributionof Y : (i)fora random sampleofsize n = 1; (ii)ifyou sample all90,000residents.