Question

suppose the approval rating for a local politician is about 42%, and so we choose a small sample of 6 citizens randomly to learn more about why they are dissatisfied with the public servant. assume the local population is large enough that choosing an individual to complete the survey does not affect the probability of selecting a new citizen that supports the politician.

what is the probability that 1or fewer citizens will say that they support the politician?

a. 28.14%   b. 20.35%   c. 19.67%   d. 91.86%

Answer 1

Solution

Given that ,

p = 0.42

1 - p = 0.58

n = 6

Using binomial probability formula ,

P(X = x) = ((n! / x! (n - x)!) * p^x * (1 - p)^{n - x}

P(X $\leq$ 1) = P(X = 0) + P(X = 1)

P(X = ) = ((6! / 0! (6 - 0)!) * 0.42⁰ * (0.58)^{6 - 0} +  ((6! / 1! (6 - 1)!) * 0.42¹ * (0.58)^{6 - 1}

=  0.0381 + 0.1654

Probability = 0.2035

= 20.35%

Option b is correct.