Question

A research company found that 11% of the people that they called agreed to participate in a survey.

Answer 1

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;

$P(X=r)=\binom{n}{r} \times p^{r}\times (1-p)^{n-r}; x = 0,1,2,3,.....$

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)  =  $n \times p$  

                            =  $196 \times 0.11$  = 21.56 ≈ 22 people

Hence, 22 people would be expected to participate in the survey.