Understanding of quantile plot versus remove outliers plot I have sample height for some people sample with a quantile plot like this: 

I need to check that the sample belongs to normal distribution.


I remove outliers
Q <- quantile(people$height, probs=c(.25, .75), na.rm = FALSE)
iqr <- IQR(people$height)
eliminated <- subset(people, people$height > (Q[1] - 1.5*iqr) & people$height < (Q[2]+1.5*iqr))

Results is: 

According to https://data.library.virginia.edu/understanding-q-q-plots/
Is correct thinking that my sample belongs to the normal distribution? Why? 
 A: Sometimes it is useful to have some visual guidance when
trying to judge whether a normal quantile plot is 'near enough'
to linear.
First, here is a demonstration how R makes plots using qqnorm.
If the data have $n$ points, then ppoints makes a vector
of $n$ points evenly spaced between $0$ and $1.$
Then for the horizontal axis, these points are transformed
by the standard normal quantile function qnorm. The vertical
axis shows the $n$ data points sorted in order from smallest
to largest.
In the program below, we simulate $n = 100$ points from
$\mathsf{Norm}(\mu=150, \sigma=9).$ First, we use
qqnorm to make a normal QQ plot of the data with
the default open circles as plotting points. Then,
we use the method described above to put orange points
into the open circles from qqnorm. They fit perfectly.
# method
set.seed(2020)
x = rnorm(100, 150, 9)
qqnorm(x)
points( qnorm(ppoints(100)), sort(x),  pch=20,col="orange" )


Now, make a normal QQ plot of normal data x (left panel below).
Perhaps you think the plot is too 'wobbly' in the tails for
the sample to be normal
We make the same QQ-plot again in the right panel.
As guidance on how well such points should conform to a straight
line, we use the method above overlay QQ-plots (in light blue) from the method above for 20 additional
normal samples with matching means and standard deviations.
Finally, for clarity, we refresh the original probability plot of
the x's.
par(mfrow = c(1,2))
set.seed(509)
 x = rnorm(100, 150, 9)
 qqnorm(x); qqline(x)

 qqnorm(x)         
  for(i in 1:20) {
   y = rnorm(100, mean(x), sd(x))
   points( qnorm(ppoints(100)), sort(y),pch=20, col="skyblue")
  }
  points(qnorm(ppoints(100)), sort(x), pch=19)  # refresh
par(mfrow=c(1,1))


It seems that the QQ-plot of the data x is not unusual for normal
samples of size $n = 100.$
Some other statistical software programs give 'confidence bands' around
quantile plots. They seem useful, but I have never understood exactly what the probability 95% refers to. Here is a plot of a normal sample of size 100, made using a recent release of Minitab.

