#Biostatistics 080

#CREATING A PSEUDORANDOM NORMAL DISTRIBUTION:
X=rnorm(1000,65,25)
hist(X,nclass=50,col="gray",border="red")

#STANDARDIZING DATA:
mu=mean(X)
sigma=sd(X)
Z=(X-mu)/sigma
Z[1:10]
hist(Z,nclass=50,col="gray",border="red")

Z2=scale(X,center=TRUE,scale=TRUE)
Z2[1:10]

#PQ FUNCTIONS FOR NORMAL DISTRIBUTION:

mu=0

sigma=1
X=1.6449

PHI=0.90
dnorm(X,mu,sigma)       # point estimate P(X) given X
pnorm(X,mu,sigma)       # cumulative phi(X) given X

qnorm(PHI,mu,sigma)   # X given cumulative phi(X)

#EXAMPLE INTERVAL CALCULATIONS:
mu=0
sigma=1

MIN=pnorm(-1,mu,sigma)
MAX=pnorm(1,mu,sigma)
MAX-MIN

MIN=pnorm(-2.576,mu,sigma)
MAX=pnorm(2.576,mu,sigma)
MAX-MIN

MIN=pnorm(-1.96,mu,sigma)
MAX=pnorm(1.96,mu,sigma)
MAX-MIN

#QUANTILES
Q=qnorm(0.975,mu,sigma)
Q

PHI=seq(0.025,0.975,0.025)
PHI

Q=qnorm(PHI,mu,sigma)
Q