Question

a/Use Excel to find the discrete probability and cumulative probability of the Binomial distribution with probability of success p = 0.75 and n = 80. Find its mean and variance. b/Based upon Excel chart, what can you conclude about the binomial convergence? Hint: Use binom.dist function on Excel and sketch the curve.

Answer 1

Find its mean and variance.

We are given n =80, p = 0.75, q = 1 – p = 1 – 0.75 = 0.25

Mean = n*p =80*0.75 = 60

Variance = n*p*q = 80*0.75*0.25 = 15

Based upon the chart on Excel, what can you conclude about the binomial convergence?

Use binom.dist function on Excel and sketch the curve.

Required excel chart and sketch is given as below:

x	P(X)
0	6.84228E-49
1	1.64215E-46
2	1.94594E-44
3	1.51784E-42
4	8.7655E-41
5	3.99707E-39
6	1.4989E-37
7	4.75366E-36
8	1.30131E-34
9	3.12315E-33
10	6.65232E-32
11	1.26999E-30
12	2.19073E-29
13	3.43776E-28
14	4.93564E-27
15	6.51504E-26
16	7.94021E-25
17	8.96777E-24
18	9.41616E-23
19	9.21792E-22
20	8.4344E-21
21	7.22948E-20
22	5.81645E-19
23	4.40027E-18
24	3.13519E-17
25	2.10685E-16
26	1.33704E-15
27	8.02223E-15
28	4.55548E-14
29	2.45054E-13
30	1.24977E-12
31	6.04729E-12
32	2.77797E-11
33	1.21221E-10
34	5.02709E-10
35	1.98211E-09
36	7.43291E-09
37	2.65174E-08
38	9.00197E-08
39	2.90833E-07
40	8.94311E-07
41	2.61749E-06
42	7.29159E-06
43	1.93312E-05
44	4.87673E-05
45	0.000117042
46	0.00026716
47	0.000579795
48	0.001195826
49	0.002342843
50	0.004357689
51	0.007690039
52	0.012866027
53	0.020391438
54	0.030587158
55	0.043378151
56	0.058095738
57	0.07338409
58	0.087301762
59	0.097659598
60	0.102542578
61	0.100861552
62	0.092727556
63	0.079480763
64	0.063336233
65	0.046771372
66	0.031889572
67	0.019990478
68	0.011465127
69	0.005981805
70	0.002819994
71	0.001191547
72	0.00044683
73	0.000146903
74	4.16887E-05
75	1.00053E-05
76	1.97473E-06
77	3.0775E-07
78	3.55096E-08
79	2.69693E-09
80	1.01135E-10

#Yes, it converges