Question

22% of US adults use Twitter. A random sample of 15 US adults is selected. a) Find the probability that the sample contains exactly 4 Twitter users. b) Find the probability that at least one US adult in the sample uses Twitter. c) Find the mean and standard deviation for the number of US adults using Twitter.

Answer 1

Given that ,

p = 0.22

1 - p = 1 - 0.22 = 0.78

n =15

Using binomial probability formula ,

P(X = x) = (n C x) * px * (1 - p)n - x

P(X =4) = (15 C 4) * 0.224 * (0.78)11

probability =0.2079

(B)

P(X 1  ) = 1 - P( x <1)

= 1 - P(X = 0)

= 1 - (15 C 0) * 0.220 * (0.78)15

=1-0.0241

probability=0.9759

(C)

Mean = = n * p = 15 *0.22 = 3.3

Mean =   =3.3

Standard deviation = = n * p * q = 15 * 0.22 *0.78 = 1.6044

Standard deviation = = 1.6044