Suppose that one observation, $N$, is obtained from a Poisson distribution with expected value $\lambda$. Ninety percent, 95 percent and 99 percent confidence intervals for the parameter $\lambda$ are given. For $N > 100$ a normal approximation with variance $N$ may be used.

Table 1: Confidence intervals for the expected value (parameter) of a Poisson random variable.

	Percent confidence
	90		95		99
$N$	Lower limit	Upper limit	Lower limit	Upper limit	Lower limit	Upper limit
0	0.00	3.00	0.00	3.69	0.00	5.30
1	0.05	4.74	0.03	5.57	0.01	7.43
2	0.36	6.30	0.24	7.22	0.10	9.27
3	0.82	7.75	0.62	8.77	0.34	10.98
4	1.37	9.15	1.09	10.24	0.67	12.59
5	1.97	10.51	1.62	11.67	1.08	14.15
6	2.61	11.84	2.20	13.06	1.54	15.66
7	3.29	13.15	2.81	14.42	2.04	17.13
8	3.98	14.43	3.45	15.76	2.57	18.58
9	4.70	15.71	4.12	17.08	3.13	20.00
10	5.43	16.96	4.80	18.39	3.72	21.40
11	6.17	18.21	5.49	19.68	4.32	22.78
12	6.92	19.44	6.20	20.96	4.94	24.14
13	7.69	20.67	6.92	22.23	5.58	25.50
14	8.46	21.89	7.65	23.49	6.23	26.84
15	9.25	23.10	8.40	24.74	6.89	28.16
16	10.04	24.30	9.15	25.98	7.57	29.48
17	10.83	25.50	9.90	27.22	8.25	30.79
18	11.63	26.69	10.67	28.45	8.94	32.09
19	12.44	27.88	11.44	29.67	9.64	33.38
20	13.25	29.06	12.22	30.89	10.35	34.67
21	14.07	30.24	13.00	32.10	11.07	35.95
22	14.89	31.41	13.79	33.31	11.79	37.22
23	15.72	32.59	14.58	34.51	12.52	38.48
24	16.55	33.75	15.38	35.71	13.26	39.74
25	17.38	34.92	16.18	36.90	14.00	41.00
26	18.22	36.08	16.98	38.10	14.74	42.25
27	19.06	37.23	17.79	39.28	15.49	43.50
28	19.90	38.39	18.61	40.47	16.25	44.74
29	20.75	39.54	19.42	41.65	17.00	45.98
30	21.59	40.69	20.24	42.83	17.77	47.21
31	22.44	41.84	21.06	44.00	18.53	48.44
32	23.30	42.98	21.89	45.17	19.30	49.67
33	24.15	44.13	22.72	46.34	20.08	50.89
34	25.01	45.27	23.55	47.51	20.86	52.11
35	25.87	46.40	24.38	48.68	21.64	53.32
36	26.73	47.54	25.21	49.84	22.42	54.54
37	27.59	48.68	26.05	51.00	23.21	55.75
38	28.46	49.81	26.89	52.16	24.00	56.96
39	29.33	50.94	27.73	53.31	24.79	58.16
40	30.20	52.07	28.58	54.47	25.59	59.36
41	31.07	53.20	29.42	55.62	26.38	60.56
42	31.94	54.32	30.27	56.77	27.18	61.76
43	32.81	55.45	31.12	57.92	27.99	62.96
44	33.69	56.57	31.97	59.07	28.79	64.15
45	34.56	57.69	32.82	60.21	29.60	65.34
46	35.44	58.82	33.68	61.36	30.41	66.53
47	36.32	59.94	34.53	62.50	31.22	67.72
48	37.20	61.05	35.39	63.64	32.03	68.90
49	38.08	62.17	36.25	64.78	32.85	70.08
50	38.96	63.29	37.11	65.92	33.66	71.27
51	39.85	64.40	37.97	67.06	34.48	72.45
52	40.73	65.52	38.84	68.19	35.30	73.62
53	41.62	66.63	39.70	69.33	36.13	74.80
54	42.51	67.74	40.57	70.46	36.95	75.97
55	43.40	68.85	41.43	71.59	37.78	77.15
56	44.29	69.96	42.30	72.72	38.60	78.32
57	45.18	71.07	43.17	73.85	39.43	79.49
58	46.07	72.18	44.04	74.98	40.26	80.66
59	46.96	73.28	44.91	76.11	41.09	81.82
60	47.85	74.39	45.79	77.23	41.93	82.99
61	48.75	75.49	46.66	78.36	42.76	84.15
62	49.64	76.60	47.54	79.48	43.60	85.32
63	50.54	77.70	48.41	80.60	44.43	86.48
64	51.43	78.80	49.29	81.73	45.27	87.64
65	52.33	79.91	50.17	82.85	46.11	88.80
66	53.23	81.01	51.04	83.97	46.95	89.96
67	54.13	82.11	51.92	85.09	47.79	91.11
68	55.03	83.21	52.80	86.21	48.64	92.27
69	55.93	84.31	53.69	87.32	49.48	93.42
70	56.83	85.40	54.57	88.44	50.33	94.58
71	57.73	86.50	55.45	89.56	51.17	95.73
72	58.63	87.60	56.34	90.67	52.02	96.88
73	59.54	88.69	57.22	91.79	52.87	98.03
74	60.44	89.79	58.11	92.90	53.72	99.18
75	61.35	90.89	58.99	94.01	54.57	100.33
76	62.25	91.98	59.88	95.13	55.42	101.48
77	63.16	93.07	60.77	96.24	56.28	102.62
78	64.06	94.17	61.66	97.35	57.13	103.77
79	64.97	95.26	62.55	98.46	57.98	104.91
80	65.88	96.35	63.44	99.57	58.84	106.06
81	66.79	97.44	64.33	100.68	59.70	107.20
82	67.70	98.53	65.22	101.78	60.55	108.34
83	68.60	99.62	66.11	102.89	61.41	109.48
84	69.51	100.71	67.00	104.00	62.27	110.62
85	70.42	101.80	67.89	105.10	63.13	111.76
86	71.34	102.89	68.79	106.21	63.99	112.90
87	72.25	103.98	69.68	107.31	64.85	114.04
88	73.16	105.06	70.58	108.42	65.72	115.17
89	74.07	106.15	71.47	109.52	66.58	116.31
90	74.98	107.24	72.37	110.63	67.44	117.45
91	75.90	108.32	73.27	111.73	68.31	118.58
92	76.81	109.41	74.16	112.83	69.17	119.71
93	77.73	110.50	75.06	113.93	70.04	120.85
94	78.64	111.58	75.96	115.03	70.91	121.98
95	79.56	112.66	76.86	116.13	71.77	123.11
96	80.47	113.75	77.76	117.23	72.64	124.24
97	81.39	114.83	78.66	118.33	73.51	125.37
98	82.30	115.91	79.56	119.43	74.38	126.50
99	83.22	117.00	80.46	120.53	75.25	127.63
100	84.14	118.08	81.36	121.63	76.12	128.76