You are on the right track. Notice that in your mixture, the uniform distribution spans [0,2], but the Normal distribution has a mean of 3. Here is another mixture. Just adjust the distribution parameters as needed:
dist = MixtureDistribution[{1, 1},
{
UniformDistribution[{0, 100}],
NormalDistribution[50, 2]
}
];
Histogram[RandomVariate[dist, 1000], {1}]
Edit: If you want data, you can use some variant of HistogramList:
{binBoundaries, counts} =
HistogramList[RandomVariate[dist, 1000], {1}];
ListPlot[Transpose[{Most[binBoundaries], counts}], PlotRange -> All,
Filling -> Axis]