Question

Sketch some Normal curves.
(a) Sketch a Normal curve that has mean 10 and standard deviation 3.
(b) On the same x axis, sketch a Normal curve that has mean 20 and standard deviation 3.
(c) How does the Normal curve change when the mean is varied but the standard deviation
stays the same?

Answer 1

(a)

The Normal Curve with mean 10 and standard deviation 3 is plotted in Red.

(b)

The Normal Curve with mean 10 and standard deviation 3 is plotted in Blue.

(c)

When the mean is varied but the standard deviation stays the same, the shape of the curve along with the spread remains same. Only the normal curve is shifted towards right with increase in mean or shifted towards left with decrease in mean.

R code -

mu = 10 ; sd = 3
x=seq(mu-3.5*sd,mu+3.5*sd,length=200)
y=dnorm(x,mean=mu,sd=sd)
plot(x,y,type="l",lwd=2,col="red", ylab = "f(x)", xlab = "x", xlim = c(0,30))
from=mu-3.5*sd
to=-mu+3.5*sd
x1=seq(from,to,length=100)
y1=dnorm(x1,mean=mu,sd=sd)

mu = 20 ; sd = 3
x=seq(mu-3.5*sd,mu+3.5*sd,length=200)
y=dnorm(x,mean=mu,sd=sd)
lines(x,y,type="l",lwd=2,col="blue", ylab = "f(x)", xlab = "x")