C no more than two people have done a one time fling 2...

Name: c no more than two people have done a one time fling 2 homework 52 question 11 about 15 of people in america use a certain social media website in a group with 20 people assume that it is a 93998
Uploaded: 2023-07-12T00:47:20-08:00
Duration: 4 min 18 s
Channel: Robin Corrigan
Description: c no more than two people have done a one time fling 2 homework 52 question 11 about 15 of people in america use a certain social media website in a group with 20 people assume that it is a 93998

(c) no more than two people have done a one-time fling #2- Homework 5.2, Question 11 About 15% of people in America use a certain social media website. In a group with 20 people (assume that it is a random sample of people in America), what are the following probabilities? (Round your answers to three decimal places.) (a)At least one of them uses the website. (b)More than two of them use the website. (c)None of them use the website. (d)At least 18 of them do not use the website.

Transcript

00:01 In this question it's stated that about 20 % of people in america use a certain social media website.

00:07 So that's a probability of 0 .20 for any randomly selected american.

00:12 And we consider a randomly selected group of 15 americans.

00:17 And we're asked for the probabilities that certain numbers of these 15 use this website.

00:23 So let's define the random variable x as the number of people in the sample of 15 who use the website.

00:29 In this situation, each of the 15 people in the sample can be viewed as bernoulli trials having two outcomes of interest, either use the website or not.

00:38 And since it's a random sample, their outcomes are independent.

00:41 The number of successes in a fixed number of independent bernoulli trials is a binomial random variable.

00:47 So here we can say x is a binomial based on 15 trials and probability of success 0 .2 on each trial.

00:56 Probability function for the binomial random variable is in general terms given by this formula.

01:14 And for part a of this question we want the probability that at least one of the 15 uses the website.

01:22 So that is we want the probability that x is greater than or equal to 1.

01:27 This can be re -expressed as 1 minus the probability that x is equal to 0.

01:33 And using the probability function, the probability that x is equal to 0 is simplified to 1 minus p, which is 0 .8, to the exponent n, which is 15.

01:46 This comes out to approximately 0 .9648...

Question

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