A realtor wants to estimate the mean price of houses in Mission Viejo, California. She collects a sample of $36$ recent house sales $($in $$1,000$ s$),$ a portion of which is shown in the accompanying table. Assume that the population standard deviation is $100($in $$1,000$ s$).($You may find it useful to reference the $z$ table.$)$

Prices $($in $$1,000$ s$)430520$ vdots $430$

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a$.$ Construct $95\%$ and $98\%$ confidence intervals for the mean price of all houses in Mission Viejo, CA$.($Round final answers to nearest whole number.$)$

$\backslash$table$[[$Confidence Level,Confidence Interval$],[95\%,,$to$],[98\%,$to$,],[,,]]$

Prices

$430$

$520$

$460$

$475$

$670$

$521$

$670$

$417$

$533$

$11,525$

$12,538$

$13,370$

$14,530$

$15,525$

$16,430$

$17,330$

$18,575$

$19,555$

$20,521$

$21,350$

$22,399$

$23,560$

$24,440$

$25,425$

$26,669$

$27,660$

$28702$

$29,540$

$30,460$

$31,588$

$32445$

$33412$

$34,735$

$35,537$

$36,630$

$37,430$

$38$

$39$

MV