Can mean() function be used to show probability of cumulative distribution function?

[skyfall]

I was doing my assignment, and I found something strange.
I did this code for question #1.
x <- heights$height[heights$sex=="Male"]

and the next question is like this:
"We will define a function "CDF" like following:
CDF <- function(a) {mean(x<=a)}
Explain why the CDF function is Cumulative Distribution Function."

I get the idea of the cumulative distribution function, but I don't get why function mean() is used there.
For example, CDF(70) equals 0.623..., which is the probability of cumulative distribution at 70. How does mean() function show probability in this function?

[StatSteph]

Hi, I think the key here is to think a bit step-by-step.

What will happen when you enter x<=a? You will get a logical vector of TRUE/FALSE values.

Then you take the mean of it. This gives you a proportion since TRUE is treated as 1 and FALSE is treated as 0.

set.seed(12345)

x <- rnorm(20)

# Let's say we want the probablity x <= a where a=0
x
#>  [1]  0.5855288  0.7094660 -0.1093033 -0.4534972  0.6058875 -1.8179560
#>  [7]  0.6300986 -0.2761841 -0.2841597 -0.9193220 -0.1162478  1.8173120
#> [13]  0.3706279  0.5202165 -0.7505320  0.8168998 -0.8863575 -0.3315776
#> [19]  1.1207127  0.2987237
x<=0
#>  [1] FALSE FALSE  TRUE  TRUE FALSE  TRUE FALSE  TRUE  TRUE  TRUE  TRUE FALSE
#> [13] FALSE FALSE  TRUE FALSE  TRUE  TRUE FALSE FALSE
mean(x<=0) # this really gives us a proportion because it is a mean of 0 and 1
#> [1] 0.5

^{Created on 2021-10-12 by the reprex package (v2.0.1)}