Random picking thanks to points on a curve

I have found this curve on a paper

I have achieved to get some points on this curve thanks to the app' automeris, however, now that I have the coordinates of several points, how can I create a distribution with them and pick (in Python if possible) randomly within my created distribution ?

Cheers, Eddie

Data =

45.0, 0.263

47.3, 0.470

51.5, 1.34

53.0, 1.86

54.3, 2.35

55.1, 2.84

55.8, 3.39

56.1, 3.88

56.6, 4.36

57.4, 5.41

57.1, 4.89

57.9, 6.41

57.6, 5.90

58.4, 7.46

58.1, 6.97

58.6, 8.49

58.6, 7.98

59.1, 10.1

59.1, 9.52

59.1, 8.99

59.9, 11.6

59.6, 11.1

59.6, 10.6

60.1, 13.1

60.1, 12.6

60.1, 12.1

60.9, 14.7

60.6, 14.2

60.7, 13.7

61.4, 15.7

61.2, 15.2

61.7, 16.7

61.7, 16.2

62.4, 17.8

62.2, 17.2

62.9, 18.7

62.7, 18.3

63.7, 19.3

64.7, 19.8

67.3, 19.8

68.3, 19.3

69.4, 18.8

70.4, 18.3

71.5, 17.8

72.8, 17.3

74.0, 16.8

75.6, 16.4

77.2, 15.9

78.2, 15.4

79.7, 14.9

81.3, 14.4

82.9, 13.9

84.7, 13.4

86.0, 13.0

87.3, 12.5

89.1, 12.0

90.1, 11.5

91.7, 11.0

92.9, 10.5

94.2, 9.99

95.8, 9.52

96.8, 9.04

98.4, 8.54

99.9, 8.03

101, 7.59

103, 7.08

105, 6.61

107, 6.13

109, 5.66

111, 5.24

112, 4.74

117, 3.92

122, 3.32

124, 3.12

128, 2.63

130, 2.46

135, 2.10

138, 1.94

142, 1.73

146, 1.52

150, 1.34

154, 1.18

163, 0.910

172, 0.712

180, 0.592

186, 1.57

186, 1.21

186, 0.858