How to plot a continuous standard normal PDF over a normalized histogram of real discrete data [closed]

Question

Below in code are two versions. I believe plot1 might be correct but not sure why its shifted to the left and how to fix it. plot2 is copied directly from the wolfman online documentation but using my own data. It doesn't look normalized and the continuous curve is almost flat. I know something is likely wrong with both of them. Please suggest edits.

Goal is to normalize histogram of probability density so that we have a mean at zero, standard deviation is 1, and total area under graph is 1. The graph should look similar to image:

raw = {1.32, 1.37, 1.43, 1.32, 1.36, 1.33, 1.38, 1.35, 1.48, 1.28, 
   1.31, 1.52, 1.51, 1.33, 1.32, 1.27, 1.35, 1.40, 1.27, 1.39, 1.50, 
   1.31, 1.34, 1.48, 1.36, 1.33, 1.40, 1.29, 1.35, 1.36, 1.33, 1.30, 
   1.28, 1.32, 1.34, 1.33, 1.29, 1.34, 1.34, 1.29, 1.35, 1.52, 1.29, 
   1.38, 1.40, 1.28, 1.36, 1.36, 1.32, 1.62, 1.36, 1.34, 1.33, 1.33, 
   1.30, 1.31, 1.33, 1.32, 1.36, 1.41};

(* plot1 almost looks correct except for shifting from mean *)
plotHistPDF[raw_, n_ : 3] := 
 Block[{len, μ, σ, bin, hist, dist},
  len = Length[raw];
  μ = Mean[raw];
  σ = StandardDeviation[raw];
  hist = Histogram[raw, Automatic, "PDF"];
  dist = Plot[
           PDF[NormalDistribution[μ, σ], x], {x, μ - n σ, μ + n σ}, 
           PlotRange -> All, Filling -> Axis];
  Show[
    hist, dist, 
    PlotLabel -> Style["Probabality Density Distribution", Bold, Orange], 
    AxesLabel -> {x, ρ}, ImageSize -> imgsize]
  ]

(* plot2 appears correctly placed but curve is flat. should be a bell shaped curve *)
Show[
  Histogram[raw, Automatic, "PDF"], 
  Plot[PDF[NormalDistribution[0, 1], x], {x, -4, 4}]
]

Answer 1

To summarize @JimB's comment, you should plot the PDF of the normal distribution that most closely resembles your data, i.e. the one with the same mean and standard deviation:

Show[
  Histogram[raw, Automatic, "PDF"],
  Plot[
    PDF[NormalDistribution @@ Through[{Mean, StandardDeviation}[raw]], x],
    {x, -4, 4}, PlotRange -> All,
    Filling -> Axis
  ]
]

---

@aooiiii also mentioned another important point. You say that the plot of the PDF is "shifted to the left and how to fix it". If you mean that the distributions seem mismatched, then you have to realize that your raw data does not appear normally distributed, with its mode a bit to the left of its mean.

Answer 2

I get this plot: followed @JimB advice. Time to learn some statistics, again.