A continous r.v.$X$ with a Normal distribution is one of the most important types of r.v.s.
Support: $-\infty ≤ x ≤ +\infty$
Two Parameters:
$\mu = E[X] = mean$
$\sigma^2 = Var(X) =$ variance, or
$\sigma =$ standard deviation
area under ANY curve will be equal to 1!
A standard normal r.v. is
$Z$ ~ Normal ( $\mu = 0, \sigma = 1$ )
mu=100; sigma=15
#dnorm, pnorm, qnorm can all be used for normal distributions
curve(dnorm(x,mean=mu,sd=sigma))
#see output 1, plots a normal distr.
pnorm(mu, mean=mu, sd=sigma)
#yields probability up to a point, here it would be the cdf@100
#output is 0.50
normprob(mu, sigma, -Inf, mu)
#see output 2, visualizes the above probability
1-pnorm() #used to get the probability above a point
pnorm(..., lower.tail=F) #yields the same as above
normprob(mean, sd, lowerBound, upperBound) #used to get probability between two points
