SOLUTION: In a survey, it was reported that 33% of women believe in the existence of aliens. If 100 women are selected at random, what is the probability that more than 45% of them will say
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Question 632572: In a survey, it was reported that 33% of women believe in the existence of aliens. If 100 women are selected at random, what is the probability that more than 45% of them will say that they believe in aliens?
Answer by reviewermath(1029) (Show Source): You can put this solution on YOUR website!
X~Binomial(100,0.33)
Look for P(46 or greater) in the table below:
The answer is .
Note: The answer is slightly different if we use Normal distribution to approximate the probability. the answer 0.0046293 is exact because all the requirements of Binomial Distribution are satisfied to solve the probability.
x P(x) P(x or fewer) P(x or greater)
0 0.0000000 0.0000000 1.0000000
1 0.0000000 0.0000000 1.0000000
2 0.0000000 0.0000000 1.0000000
3 0.0000000 0.0000000 1.0000000
4 0.0000000 0.0000000 1.0000000
5 0.0000000 0.0000000 1.0000000
6 0.0000000 0.0000000 1.0000000
7 0.0000000 0.0000000 1.0000000
8 0.0000000 0.0000000 1.0000000
9 0.0000000 0.0000000 1.0000000
10 0.0000001 0.0000001 1.0000000
11 0.0000002 0.0000003 0.9999999
12 0.0000009 0.0000012 0.9999997
13 0.0000029 0.0000041 0.9999988
14 0.0000088 0.0000129 0.9999959
15 0.0000250 0.0000379 0.9999871
16 0.0000654 0.0001033 0.9999621
17 0.0001591 0.0002624 0.9998967
18 0.0003614 0.0006239 0.9997376
19 0.0007683 0.0013921 0.9993761
20 0.0015325 0.0029247 0.9986079
21 0.0028756 0.0058003 0.9970753
22 0.0050859 0.0108862 0.9941997
23 0.0084952 0.0193814 0.9891138
24 0.0134243 0.0328057 0.9806186
25 0.0201004 0.0529061 0.9671943
26 0.0285583 0.0814644 0.9470939
27 0.0385513 0.1200157 0.9185356
28 0.0495043 0.1695200 0.8799843
29 0.0605364 0.2300564 0.8304800
30 0.0705656 0.3006220 0.7699436
31 0.0784817 0.3791037 0.6993780
32 0.0833502 0.4624539 0.6208963
33 0.0845942 0.5470481 0.5375461
34 0.0821062 0.6291543 0.4529519
35 0.0762590 0.7054133 0.3708457
36 0.0678174 0.7732306 0.2945867
37 0.0577774 0.8310080 0.2267694
38 0.0471796 0.8781876 0.1689920
39 0.0369420 0.9151296 0.1218124
40 0.0277479 0.9428775 0.0848704
41 0.0200003 0.9628778 0.0571225
42 0.0138381 0.9767159 0.0371222
43 0.0091934 0.9859093 0.0232841
44 0.0058659 0.9917753 0.0140907
45 0.0035954 0.9953707 0.0082247
46 0.0021174 0.9974881
47 0.0011982 0.9986863 0.0025119
48 0.0006516 0.9993379 0.0013137
49 0.0003406 0.9996785 0.0006621
50 0.0001711 0.9998497 0.0003215
51 0.0000826 0.9999323 0.0001503
52 0.0000383 0.9999706 0.0000677
53 0.0000171 0.9999877 0.0000294
54 0.0000073 0.9999951 0.0000123
55 0.0000030 0.9999981 0.0000049
56 0.0000012 0.9999993 0.0000019
57 0.0000005 0.9999997 0.0000007
58 0.0000002 0.9999999 0.0000003
59 0.0000001 1.0000000 0.0000001
60 0.0000000 1.0000000 0.0000000
61 0.0000000 1.0000000 0.0000000
62 0.0000000 1.0000000 0.0000000
63 0.0000000 1.0000000 0.0000000
64 0.0000000 1.0000000 0.0000000
65 0.0000000 1.0000000 0.0000000
66 0.0000000 1.0000000 0.0000000
67 0.0000000 1.0000000 0.0000000
68 0.0000000 1.0000000 0.0000000
69 0.0000000 1.0000000 0.0000000
70 0.0000000 1.0000000 0.0000000
71 0.0000000 1.0000000 0.0000000
72 0.0000000 1.0000000 0.0000000
73 0.0000000 1.0000000 0.0000000
74 0.0000000 1.0000000 0.0000000
75 0.0000000 1.0000000 0.0000000
76 0.0000000 1.0000000 0.0000000
77 0.0000000 1.0000000 0.0000000
78 0.0000000 1.0000000 0.0000000
79 0.0000000 1.0000000 0.0000000
80 0.0000000 1.0000000 0.0000000
81 0.0000000 1.0000000 0.0000000
82 0.0000000 1.0000000 0.0000000
83 0.0000000 1.0000000 0.0000000
84 0.0000000 1.0000000 0.0000000
85 0.0000000 1.0000000 0.0000000
86 0.0000000 1.0000000 0.0000000
87 0.0000000 1.0000000 0.0000000
88 0.0000000 1.0000000 0.0000000
89 0.0000000 1.0000000 0.0000000
90 0.0000000 1.0000000 0.0000000
91 0.0000000 1.0000000 0.0000000
92 0.0000000 1.0000000 0.0000000
93 0.0000000 1.0000000 0.0000000
94 0.0000000 1.0000000 0.0000000
95 0.0000000 1.0000000 0.0000000
96 0.0000000 1.0000000 0.0000000
97 0.0000000 1.0000000 0.0000000
98 0.0000000 1.0000000 0.0000000
99 0.0000000 1.0000000 0.0000000
100 0.0000000 1.0000000 0.0000000
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