Respuesta :
Answer:
11
Step-by-step explanation:
A marketing researcher selects the residents until the resides who have seen a theater production is selected. This statements demonstrates that experiment is repeated a variable number of time until first success is achieved so, the experiment conducted is a geometric experiment.
The quantity 9% shows the probability of success and so p=0.09.
The probability distribution function of geometric distribution is
[tex]P(X=n)=pq^{n-1}[/tex]
The mean of geometric distribution is μ=1/p.
The expected number of residents the researcher will need to ask
[tex]E(x)=mean=\frac{1}{p}[/tex]
[tex]E(x)=\frac{1}{0.09} =11.11[/tex]
Thus expected number of residents the researcher will need to ask are 11 residents.
Using the binomial distribution, it is found that the expected number of residents the researcher will need to ask to find someone who has seen the production is of 11.1.
For each resident, there are only two possible outcomes, either they have seen the production, or they have not. The probability of a resident having seen the production is independent of any other resident, hence, the binomial distribution is used to solve this question.
- The binomial probability distribution gives the probability of exactly x successes on n repeated trials, with p probability.
- The expected number of trials until r successes is given by:
[tex]E = \frac{r}{p}[/tex]
In this problem:
- Approximately 9 percent of the residents of a large city have seen a certain theater production that is currently playing in the city, hence [tex]p = 0.09[/tex].
We want one resident, hence [tex]r = 1[/tex], and:
[tex]E = \frac{r}{p} = \frac{1}{0.09} = 11.1[/tex]
The expected number of residents the researcher will need to ask to find someone who has seen the production is of 11.1.
A similar problem also involving the binomial distribution is given at https://brainly.com/question/25644451
