# P(Z<1.25),P(Z>1),P(Z>-1.08),P(0<Z<2),P(Z>2.02)

pnorm(1.25)
pnorm(1,lower.tail=F); 1-pnorm(1)
pnorm(-1.08,lower.tail=F); 1-pnorm(-1.08)
pnorm(2)-pnorm(0)
pnorm(2.02,lower.tail=F); 1-pnorm(2.02); pnorm(-2.02)

# Find the z-scores associated with: bottom 5%, top 7%, Q1, median, Q3
qnorm(.05)
qnorm(.93); qnorm(.07,lower.tail=F)
qnorm(.25)
qnorm(.5)
qnorm(.75)

# X ~ N(mu,sigma)=X~N(27,2)
# Find P(X<29),P(X>34),P(X<21),P(22<X<32),P(20<X<26)
# you can either calculate a z score and use with pnorm()
# or use the mu and sigma input options in pnorm()

mu=27; s=2
z=(29-mu)/s; pnorm(z)
# or
pnorm(29,mu,s); pnorm(29,27,2)
pnorm(34,mu,s,lower.tail=F); 1-pnorm(34,mu,s)
pnorm(32,mu,s)-pnorm(22,mu,s)
pnorm(26,mu,s)-pnorm(20,mu,s)

# X~N(mu,sigma)=X~N(27,2)
# Find the X values for: bottom 2%, top 10%, Q1, median, Q3, IQR=(Q3-Q1)
# Z=(X-mu)/sigma solving for X: X=Z(sigma)+mu

z=qnorm(.02); z; z*s+mu
# OR (easier...fewer steps)
qnorm(.02,mu,s)
z=qnorm(.1,lower.tail=F); z; z*s+mu
# OR
qnorm(.1,mu,s,lower.tail=F)

z=qnorm(.25); z; z*s+mu
# OR
qnorm(.25,mu,s)

z=qnorm(.75); z; z*s+mu
# OR
qnorm(.75,mu,s)
i.q.r=qnorm(.75,mu,s)-qnorm(.25,mu,s); i.q.r


z=qnorm(.5); z; z*s+mu
# OR
qnorm(.5,mu,s)