Shifting fit and its data on x axis

I have the following list:

l={{46, 1714.29}, {47, 2857.14}, {48, 3714.29}, {49, 5428.57}, {50,
8928.57}, {51, 8928.57}, {52, 11571.4}, {53, 14571.4}, {54,
17785.7}, {55, 25000.}, {56, 29571.4}, {57, 34214.3}, {58,
39214.3}, {59, 44142.9}, {60, 49928.6}, {61, 55714.3}, {62,
62214.3}, {63, 69571.4}, {64, 76285.7}, {65, 76285.7}, {66,
93571.4}, {67, 104071.}, {68, 114000.}, {69, 121143.}, {70,
127786.}, {71, 137214.}, {72, 144929.}, {73, 153143.}, {74,
153143.}, {75, 167571.}, {76, 167571.}, {77, 178214.}, {78,
183071.}, {79, 186786.}, {80, 188643.}, {81, 191571.}, {82,
194786.}, {83, 197214.}, {84, 200214.}, {85, 202500.}, {86,
205071.}, {87, 207286.}, {88, 209357.}, {89, 211357.}, {90,
213286.}, {91, 214857.}, {92, 216000.}, {93, 217571.}, {94,
218286.}, {95, 218714.}, {96, 219643.}}


To find the normal distribution fit I do,

FindFit[l[[All, 2]],
a PDF[NormalDistribution[\[Mu], \[Sigma]], x], {a, \[Mu], \[Sigma]},
x]


Then I plot them using:

Show[ListPlot[l[[All, 2]], PlotStyle -> Red],
Plot[9.492714442567708*^6 PDF[
NormalDistribution[44.10417734334825, 17.28548314618452],
x], {x, 0, 200}]]


As you can see they are both starting on 0. This is because I used l[[All, 2]], I wonder how can I move data and the fit to start from x=46 and onwards, to be consistent with x values of list l$$$$.

• I'm curious as to the reason for not using the full dataset: sol = FindFit[l, a PDF[NormalDistribution[\[Mu], \[Sigma]], x], {{a, 10^5}, {\[Mu], 40}, {\[Sigma], 20}}, x] followed by Show[ListPlot[l, PlotStyle -> Red], Plot[a PDF[NormalDistribution[\[Mu], \[Sigma]], x] /. sol, {x, 0, 200}]].
– JimB
Commented Mar 22, 2020 at 5:42

{minx, maxx} = MinMax@l[[All, 1]];
fit = FindFit[l[[All, 2]], a PDF[NormalDistribution[μ, σ], x], {a, μ, σ},   x];


Use the option DataRange in ListPlot and shift the argument x in the first argument of Plot by -minx:

Show[ListPlot[l[[All, 2]], PlotStyle -> Red, DataRange -> {minx, maxx}],
Plot[a PDF[NormalDistribution[μ, σ], x - minx] /. fit, {x, 0, 150}]]


I just solved it, this can be done using:

Show[ListPlot[l],
Plot[9.492714442567708*^6 PDF[
NormalDistribution[44.10417734334825, 17.28548314618452],
x], {x, 0, 200}] /. l_Line :> Translate[l, {46, 0}]]