Answer:
22 people would be expected to participate in the survey.
Step-by-step explanation:
We are given that a research company found that 11% of the people that they called agreed to participate in a survey.
The company called 196 people and we have to find that how many would be expected to participate in the survey.
The above situation can be represented through binomial distribution;
[tex]P(X=r)=\binom{n}{r} \times p^{r}\times (1-p)^{n-r}; x = 0,1,2,3,.....[/tex]
where, n = number of trials (samples) taken = 196 people
r = number of success
p = probability of success which in our question is probability
that people agreed to participate in a survey, i.e; p = 11%
Let X = Number of people who agreed to participate in a survey
SO, X ~ Binom(n = 196, p = 0.11)
Now, the expected number of people who would participate in the survey is given by;
E(X) = [tex]n \times p[/tex]
= [tex]196 \times 0.11[/tex] = 21.56 ≈ 22 people
Hence, 22 people would be expected to participate in the survey.
