1. Construction of confidence intervals a) Drawing picture show that if Z~N(0,1) (a random variable that is normally distributed with mean 0 and variance 1), then P(-za/2 30 ; X-H Z = ~ N(0, 1) plug...

I am just needing help with part c and d

30. Also in case n<30 and="" population="" standard="" deviation="" is="" known="" this="" formula="" is="" still="" valid="" given="" the="" underlying="" distribution="" of="" each="" sample="" observation="" is="" normal.="" te="" p–="" p="" c)="" using="" item="" a)="" and="" the="" central="" limit="" theorem="" of="" sample="" proportion="" which="" is="" show="" that="" z="-" n(0,="" 1)="" p(p="" –="" 2=""><>
Extracted text: 1. Construction of confidence intervals a) Drawing picture show that if Z~N(0,1) (a random variable that is normally distributed with mean 0 and variance 1), then P(-za/2 < z="">< %a/2)="1" –="" a="" b)="" by="" central="" limit="" theorem="" we="" know="" for="" n=""> 30 ; X-H Z = ~ N(0, 1) plug in this Z in the formula of a) and show that P(X – za/2" Vn <>< x="" +%a/2)="1-a" vn="" note="" that="" this="" is="" the="" formula="" for="" confidence="" interval="" of="" population="" mean="" when="" sample="" is="" large="" and="" population="" standard="" deviation="" is="" known.="" this="" would="" be="" the="" same="" as="" if="" population="" standard="" deviation="" was="" unknown="" and="" we="" were="" to="" use="" sample="" standard="" deviation,="" while="" n="">30. Also in case n<30 and="" population="" standard="" deviation="" is="" known="" this="" formula="" is="" still="" valid="" given="" the="" underlying="" distribution="" of="" each="" sample="" observation="" is="" normal.="" te="" p–="" p="" c)="" using="" item="" a)="" and="" the="" central="" limit="" theorem="" of="" sample="" proportion="" which="" is="" show="" that="" z="-" n(0,="" 1)="" p(p="" –="" 2="">< p>