Question

 

A recent study shows that 18% of adults in the US do not use the Internet. Suppose that 12 adults are randomly selected in the US.

a)Construct the PMF of X, the number of adults who don't use internet in this group.

b)What is the expected value and standard deviation of X?

c)What is the probability that at least 1 of the adults uses the Internet?

Answer 1

X ~ B ( n = 12 , P = 0.18 )

Excel function - BINOM.DIST(number_s,trials,probability_s,cumulative)

Where, number_s :- Random variable X

trials :- n = 12

probability_s = 0.18

  cumulative :- False ( if we need to find the exact probability, else true always)

  

Part a)

Probability mass function is  

X	P ( X )
0	0.0924
1	0.2434
2	0.2939
3	0.2151
4	0.1062
5	0.0373
6	0.0096
7	0.0018
8	0.0002
9	0
10	0
11	0
12	0
Total	1

Part b)

Mean = n * P = ( 12 * 0.18 ) = 2.16
Variance = n * P * Q = ( 12 * 0.18 * 0.82 ) = 1.7712
Standard deviation = (variance) = (1.7712) = 1.3309

Part c)

Here probability of not using internet is 18% i.e P = 0.18

Probability of using internet is 1 - 0.18 = 0.82

Excel function = 1 - BINOM.DIST(0,12,0.82,TRUE) = 1.00

The probability that at least 1 of the adults uses the Internet is 1.00