Question

According to the 2009 current Population Survey conducted by the U.S. Census Bureau, 40% of the U.S. population 25 years old and over have completed a bachelor's degree or more. Given a random sample of 50 people 25 years old or over, what is the chance that 18 or more has completed a bachelors degree?

Answer 1

Let X be the number of people 25 years old and over who have completed a bachelors degree.

X ~ Binomial(50,0.40)

Here is the probability distribution:

x	P(X=x)
0	0.000000
1	0.000000
2	0.000000
3	0.000000
4	0.000000
5	0.000002
6	0.000011
7	0.000047
8	0.000169
9	0.000527
10	0.001440
11	0.003491
12	0.007563
13	0.014738
14	0.025967
15	0.041547
16	0.060589
17	0.080785
18	0.098737
19	0.110863
20	0.114559
21	0.109103
22	0.095879
23	0.077815
24	0.058361
25	0.040464
26	0.025938
27	0.015371
28	0.008417
29	0.004257
30	0.001987
31	0.000854
32	0.000338
33	0.000123
34	0.000041
35	0.000012
36	0.000003
37	0.000001
38	0.000000
39	0.000000
40	0.000000
41	0.000000
42	0.000000
43	0.000000
44	0.000000
45	0.000000
46	0.000000
47	0.000000
48	0.000000
49	0.000000
50	0.000000

We have to find the probability

P(X>=18) = 0.763124198799121

There is a 76.31% chance.

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