Question

According to CNN/USA Today poll appox. 70% of Americans believe the IRS abuses its power. Let X equal the number of people who believe the IRS abuses its power in a sample of n=25 Americans. Assuming that the poll results are still valid , find the probability that a) X is at least 13 b) X is at most 11 c) x is equal to 12 d) give the mean, variance, and standard deviation of X use the binomial probability tables, how do you use values above 0.5 such as 0.7

Answer 1

Ans:

Given that

n=25,p=0.70

P(x=r)=25C_r*0.7^r*(1-0.7)^25-r

x	p(x)
1	0.0000
2	0.0000
3	0.0000
4	0.0000
5	0.0000
6	0.0000
7	0.0000
8	0.0001
9	0.0004
10	0.0013
11	0.0042
12	0.0115
13	0.0268
14	0.0536
15	0.0916
16	0.1336
17	0.1651
18	0.1712
19	0.1472
20	0.1030
21	0.0572
22	0.0243
23	0.0074
24	0.0014
25	0.0001

Use above table for calculations:

a)P(atleast 13)=P(x>=13)

=P(x=13)+P(x=14)+...............+P(x=25)

=0.0268+0.0536+….+0.0001

=0.9825

b)P(x<=11)=P(x=0)+P(x=1)+.............+P(x=11)

=0.0000+0.0000+.............+0.0042

=0.0060

c)

P(x=12)=0.0115

d)

mean=np=25*0.7=17.5

Variance=np(1-p)=25*0.7*0.3=5.25

standard deviation=sqrt(5.25)=2.29