Question

A political scientist wants to conduct a research study on a president's approval rating. The researcher has obtained data that states that 45% of citizens are in favor of the president. The researcher wants to determine the probability that 6 out of the next 8 individuals in his community are in favor of the president. What is the binomial coefficient of this study? Write the answer as a number, like this: 42.

Answer 1

28

Explanation:

Answer 2

The probability that 6 out of the next 8 individuals in his community are in favor of the president.

P( X=6) = 0.070 or 7 percentage

Explanation:

Step(i):-

Given data the researcher has obtained data that states that 45% of citizens are in favor of the president

probability of success 'p' = 45% or 0.45

q = 1-0.45 = 0.55

Given random sample size 'n' = 8

Let 'X' be the random variable

let 'X' = 6

`P(X=r) = n_{C_(r) } (p)^(r) (q)^(n-r)`

The probability that 6 out of the next 8 individuals in his community are in favor of the president.

`P(X=6) = 8_{C_(6) } (0.45)^(6) (0.55)^(8-6)`

`8_{C_(6) } = (8!)/((8-6)!6!) = (8 X 7 X 6!)/(2 X 1 X 6!) =(8 X 7)/(2 x1) = 28`

P( X=6) = 28 × 0.00830 ×0.3025

P( X=6) = 0.070

Conclusion:-

The probability that 6 out of the next 8 individuals in his community are in favor of the president.

P( X=6) = 0.070 or 7 percentage