Question

Use Excel/Megastat to find the discrete probability and cumulative probability of the Binomial distribution with probability of success p = 0.3 and n = 70.

Find its mean and variance.

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

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

Answer 1

Find its mean and variance.

We are given n = 70, p = 0.3, q = 1 – p = 1 – 0.3 = 0.7

Mean = n*p = 70*0.3 = 21

Variance = n*p*q = 70*0.3*0.7 = 14.7

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:

From above sketch it is observed that the binomial distribution is converges to the approximate normal distribution.

Excel chart:

X	P(X)	CDF
0	0.000000	0.000000
1	0.000000	0.000000
2	0.000000	0.000000
3	0.000000	0.000000
4	0.000000	0.000001
5	0.000003	0.000003
6	0.000012	0.000015
7	0.000046	0.000060
8	0.000154	0.000215
9	0.000455	0.000670
10	0.001190	0.001860
11	0.002782	0.004642
12	0.005862	0.010504
13	0.011208	0.021712
14	0.019558	0.041270
15	0.031292	0.072562
16	0.046100	0.118662
17	0.062758	0.181420
18	0.079195	0.260615
19	0.092890	0.353505
20	0.101516	0.455020
21	0.103587	0.558608
22	0.098879	0.657486
23	0.088438	0.745925
24	0.074225	0.820150
25	0.058532	0.878681
26	0.043416	0.922098
27	0.030323	0.952420
28	0.019957	0.972377
29	0.012387	0.984764
30	0.007255	0.992020
31	0.004012	0.996032
32	0.002096	0.998128
33	0.001034	0.999162
34	0.000482	0.999644
35	0.000213	0.999857
36	0.000089	0.999945
37	0.000035	0.999980
38	0.000013	0.999993
39	0.000005	0.999998
40	0.000002	0.999999
41	0.000000	1.000000
42	0.000000	1.000000
43	0.000000	1.000000
44	0.000000	1.000000
45	0.000000	1.000000
46	0.000000	1.000000
47	0.000000	1.000000
48	0.000000	1.000000
49	0.000000	1.000000
50	0.000000	1.000000
51	0.000000	1.000000
52	0.000000	1.000000
53	0.000000	1.000000
54	0.000000	1.000000
55	0.000000	1.000000
56	0.000000	1.000000
57	0.000000	1.000000
58	0.000000	1.000000
59	0.000000	1.000000
60	0.000000	1.000000
61	0.000000	1.000000
62	0.000000	1.000000
63	0.000000	1.000000
64	0.000000	1.000000
65	0.000000	1.000000
66	0.000000	1.000000
67	0.000000	1.000000
68	0.000000	1.000000
69	0.000000	1.000000
70	0.000000	1.000000