Question

A survey shows that 81% of households in the United States own a computer. You randomly select 12 households and ask if they own a computer. Answer the following questions. 1) Identify n 2) Identify p 3) Calculate 1 - p 4) Find the probability that exactly 6 of them respond yes 5) Find the probability that at least 6 of them respond yes 6) Find the probability that fewer than 6 of them respond yes 7) Find the probability that between 5 and 10 of them (inclusive) respond yes 8) Find the probability that no more than 8 of them respond yes 9) Find the probability that more than 9 of them respond yes 10) What is the expected (mean) number of “yes” response? 11) What is the standard deviation of the expected (mean) number of “yes” response?

Answer 1

1) Identify n

12

2) Identify p

81%

3) Calculate 1 - p

1-81% = 19%

To answer the following question, let us first describe the distribution of X, where X is the number of people who own a computer.

X ~ Binomial(12,0.81) with the following probability distribution:

X	P(X=x)
0	0.000000002
1	0.000000113
2	0.000002655
3	0.000037728
4	0.000361888
5	0.002468457
6	0.012277323
7	0.044863001
8	0.119536285
9	0.226489803
10	0.289668537
11	0.224527766
12	0.079766443

4) Find the probability that exactly 6 of them respond yes

P(X=6) = 0.01227732324

5) Find the probability that at least 6 of them respond yes

P(X>=6) = 0.997129157522091

6) Find the probability that fewer than 6 of them respond yes 7)

P(X<6) = 1 -0.997129157522091 = 0.00287084247790914

Find the probability that between 5 and 10 of them (inclusive) respond yes

P(5<=X<=10) = 0.695303405271898

8) Find the probability that no more than 8 of them respond yes

P(X<=8) = 0.179547451227308

9) Find the probability that more than 9 of them respond yes

P(X>9) = 0.593962746002227

10) What is the expected (mean) number of “yes” response?

E(X) = n * p = 12 * 0.81 = 9.72

11) What is the standard deviation of the expected (mean) number of “yes” response?

SD(X) = (n * p * (1-p))^0.5 = (1.8468)^0.5 = 1.35897019834874

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