Standard deviation in probability distribution (pnorm)

General
1

Hey! I'm a complete R beginner and I've been struggling with understanding the logic behind SD in probability distributions. I read from "Applied Statistics with R" that SD is related to σ^2. Examples:

  #>calculate P(X≤5), when X ∼ N(4,16)
  pnorm(5, mean = 4, sd = 4)

  #>calculate P(X≤3), when X ∼ N(2,25)
  pnorm(3, mean = 2, sd = 5)

To my understanding the SDs in the codes have been attained by taking the square root of the last parameter inside brackets. But why can't I just use 16 or 25 in the code? I also keep running into problems with practical exercises where the parameters are X ∼ N(0,1) - unfortunately I cannot give details as my RStudio seems executes the code correctly, but for whatever reason the answer is "incorrect" according to my course platform.

I've been through multiple websites and blogs as well the R Studio's help section, yet I cannot find information that would clearly explain to me how to "adjust" the SD according to the parameters given in the form of X ∼ N(n1,n2). Any insight would be greatly appreciated!

2

Maybe the normal distribution is denoted as N(μ,σ²). And the parameters is μ, σ. I am also an R beginner, just know little about it, sorry.

3

in the notation "N(4,16)", 16 stands for variance, the square of standard deviation. but the pnorm function needs standard deviation.
difference between variance and standard deviation can be found in the following link

4

why would your code running without throwing errors leave you unable to provide details as to supposed incorrect answers to concrete questions ?

5

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