In Exercises 21-28, find the probability and answer the questi...

Question

In Exercises 21-28, find the probability and answer the questions.

Social Networking In a Pew Research Center survey of Internet users, 3732 respondents say that they use social networking sites and 1380 respondents say that they do not use social networking sites. What is the probability that a randomly selected person uses a social networking site? Does that result suggest that it is likely (with a probability of 0.5 or greater) for someone to use social networking sites?

Accepted Answer

Hello there. Today we're gonna solve the following practice problem together. So first off, let us read the problem and highlight all the key pieces of information that we need to use in order to solve this problem. In a survey of media consumption habits, 2,865 individuals reported that they subscribe to at least one streaming service, while 1,045 said they do not subscribe to any streaming services. What is the probability that a randomly chosen subject? Is a subscriber to streaming services round the answer to three decimal places, does that probability indicate that it is likely with a probability of 0.5 or greater for someone to subscribe to streaming services? Awesome. So it appears for this particular problem, we're ultimately trying to solve for two separate answers. Our first answer is we're asked to determine what the probability of a randomly chosen subject will be a subscriber to a streaming service. And our second answer we're trying to solve for other than the probability, is we're trying to determine yes or no. Does that probability indicate that is likely? With a probability of 0.5 or greater for someone to subscribe to a streaming service. So now that we know that we're ultimately trying to solve for two separate answers, let's read off our multiple choice answers to see what our final answer pair might be. A is 0.854 and no. B is 0.733, and yes. C is 0.692 and no, and finally D is 0.575 and yes. Awesome. So first off, in order to solve for this particular problem, we need to understand all of our information that we provided. So we need to note once again that we're told that 2,865 people are subscribers to streaming services. I'll put a S in quotation marks to mean that they're subscribed, and we also need to note that there is 1000. 45 individuals who are not subscribed, so I'll call it NS for short in quotation marks. So, 2,865 are subscribers to streaming services and 1,045 individuals or A around, you know, our subscribers are not subscribed, so we have a certain amount of subscribers and then individuals that are not subscribed. So, moving right along here, that's our first step. is determining our information that we are given. Our second step that we need to take is we need to determine the total number of people surveyed. So as we should recall, the total number of people surveyed, which I'll call T for total, it's going to be equal to 2,865 plus 1,045. So when we add Those two numbers together we will get 3910. So now our 3rd step is we need to find the probability that a randomly selected individual subscribes to a streaming service. So, P P of S, so where S denotes subscribers, so the probability that someone is a subscriber, so P of S is equal to 2,865 divided by 3910. So if we take 2,865 and we divide it by 3910, we will find when we round to three decimal places, because we're asked to, by the problem itself, to round our answer to three decimal places. You will find that it's approximately equal to 0.733, and that is our final answer. Hooray, we did it for the probability. So our probability is 0.733. So now we need to solve for our final answer for our yes or no. Does that probability indicate that it is likely for someone to subscribe to a streaming service? So now we need to interpret our result, so we need to note that since the probability is 0.733, Which is greater than 0.5, so this value is greater than 0.5. So that means that as a result, it suggests that it is likely someone subscribes to at least one streaming service, so our second answer will be yes. So it appears, without a doubt, our final answer has to be multiple choice answer letter B, which once again is 0.733 and yes. Thank you so much for watching. Hopefully that helped and I can't wait to see you in the next video. Bye.

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Key Concepts

Probability

Sample Size

Statistical Significance

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